(2) The Israelites shall camp each [household] with its standard, under the banners of their ancestral house; they shall camp around the Tent of Meeting at a distance.

באתת [EVERY MAN OF THE CHILDREN OF ISRAEL SHALL ENCAMP BY HIS OWN STANDARD] WITH THE SIGNS [OF THEIR FATHERS’ HOUSES] — Each banner shall have a different sign — a piece of coloured cloth hanging on it, the colour of the one not being the same as the colour of another, but the colour of each tribe shall be like that of his stone that is fixed in the breastplate (of. Exodus 28:21), and by this means everybody will be able to recognise his banner . Another explanation of באתת לבית אבתם is: by the signs (i.e., following the signs) which their father Jacob gave them severally when they carried him out from Egypt.

You, O Judah, your brothers shall praise;Your hand shall be on the nape of your foes;Your father’s sons shall bow low to you.

And of Gad he said:
Blessed be the One who enlarges Gad!Poised is he like a lionTo tear off arm and scalp.

Like a firstling bull in his majesty,He has horns like the horns of the wild-ox;With them he gores the peoples,The ends of the earth one and all.These are the myriads of Ephraim,Those are the thousands of Manasseh.

And of Dan he said:
Dan is a lion’s whelpThat leaps forth from Bashan.

What seems most reasonable to me is to say that they are arranged according to the four levels that encompass all human perfection, which are: the acquisition of wisdom, followed by the acquisition of good character traits, followed by the acquisition of strength, and after all of these, the acquisition of wealth.

Judah, Issachar, Zebulun shall journey first, for from them the Torah will emanate. Therefore, the double expression forward to the east is stated to indicate that from them the light of Torah will shine forth. For regarding Judah, it is said The scepter shall not depart from Judah, nor the ruler’s staff from between his feet (Genesis 49:10). These refer to the heads of the exile and the princes of the Land of Israel (Sanhedrin 5a, see there). And ruler’s staff [mechokek] refers only to Torah, as it says about Moses For there the portion of the lawgiver was safeguarded (Deuteronomy 33:21). And it is written Lest they drink and forget what has been decreed (Proverbs 31:5). And encamping next to him is the tribe of Issachar, about whom it is said And from the children of Issachar, those who had understanding of the times (1 Chronicles 12:32). [Then] the tribe of Zebulun, about whom it is said And from Zebulun, those who wield the writer’s staff (Judges 5:14). Furthermore, [Zebulun] would support Issachar, and therefore it does not say “and beside him the tribe of Zebulun,” because [the text] did not want to make him secondary to the tribe of Issachar, to teach that the one who learns Torah and the one who supports Torah learners are equally important. And it says about them they shall journey first, for they have the right of precedence in war, because the wars of Israel are not [fought] with sword and spear, but rather they need to be armed with the five books of the Torah, which are divided into seven books, meaning “armed,” and it [the Torah] is comprised of 27 letters, which is the numerical value of the first letters of Judah, Issachar, Zebulun, to tell you that the merit of Torah assists them in war, and they are the head of the banner that indicates victory.

The banner of the camp of Reuben, Simeon, Gad on the south side, which is called “south” [darom] based on the term “dar rom” [dwells on high], as the sun dwells in the heights. Similarly, whoever humbles himself by nature, eventually the Holy One, Blessed be He, elevates him. Humility is the foremost of all good traits. This quality was found in Reuben, for he admitted without embarrassment to the incident with Bilhah, as our Sages said (see Sotah 7b), “What caused Reuben to confess, etc.,” as Rashi brings in the portion of V’zot HaBracha (33:7). This stemmed from the trait of humility, for every proud person is embarrassed to admit the truth. And from Simeon came teachers, scribes, and the poor, among whom humility is more commonly found than in others. Similarly, Gad was charitable, as it is said about him He executed the righteousness of the Lord, and His judgments with Israel (Deuteronomy 33:21). This means that according to the letter of the law, he only needed to go with Israel and not at the head of the armed forces. But as an act of charity, he went before them, like the charity of the Lord who goes before the camp of Israel. And lest you say that perhaps they went at the head out of arrogance, the verse states Gad, a troop shall overcome him, but he shall overcome at the last [akev] (Genesis 49:19). The troop went with humility like the “heel” [akev], which signifies humility, as it is said Following [ekev] humility is the fear of the Lord (Proverbs 22:4).

The banner of the camp of Ephraim, Manasseh, and Benjamin is to the west, and they shall journey third. For the attribute of strength is third, and it is written about them, Before Ephraim and Benjamin and Manasseh, stir up Your might, etc. (Psalms 83). For Joseph is the firstborn of his ox (Deuteronomy 33:17), who possesses strength and might, and Benjamin is a wolf that tears (Genesis 49:27). And this quality diminishes progressively, as day by day a person’s strength wanes due to the melting of the essential moisture, for the day of death begins from the day of birth. Therefore, their encampment is on the western side, because in that direction the sun continues to diminish.

The banner of the camp of Dan, Asher, Naphtali to the north. From there gold comes, and all three of them were wealthy, as it is said From Asher comes rich food (Genesis 49:20), and it is written Naphtali is satisfied with favor and full of the blessing of the Lord (Deuteronomy 33:23), which makes one wealthy. And the tribe of Dan made golden calves because of the abundance of gold that was bestowed upon them, and therefore they were the gatherer for all the camps. And this acquisition is the least valuable of all, therefore it says about them they shall travel last and the faces of all were turned toward the Divine Presence in the middle, for all are equally good when they are used for the sake of Heaven. And Judah is the head of a banner because he is king and is called a lion’s whelp. Therefore, it is his role to go at the front in battle, and similarly Dan is a lion’s whelp. He went at the rear because the main battle is at the front and the rear, and Reuben the firstborn is the head of a banner, and similarly Ephraim is the head of a banner because Joseph is the firstborn.

איש על דגלו באותות, “each man by his flag according to the insignia.” The word אותות is used here in the same sense as in Jeremiah 10,2 where it is a reference to changes in the constellations in the skies. Each flag had different symbols, such as the flag of the camp of Reuven depicting דודאים, which looked like miniature human beings. The flag of Yehudah depicted a lion cub seeing his father had compared him to that animal (in fearlessness). The flag of Ephrayim bore the picture of an ox, seeing that Yaakov had likened Joseph to an ox in Genesis 49,9. The flag of Dan bore the image of an eagle. When you combine the four images depicted on these flags they were the same as that of the chayot which were part of the vision of Ezekiel who described these creatures or angels with such heads, as supporting the throne of G’d (Ezekiel chapter 1). (These are the views of both Ibn Ezra and Nachmanides).

“With the insignias” – there were insignias for each and every prince: a banner with a color for each, and every banner like the color of the gems that were on Aaron’s heart, from which the empire learned to make a banner, with colors for each and every banner. For each and every tribe, the prince’s banner was like the color of his stone. Reuben, its stone was a ruby and its banner was dyed red, and mandrakes were depicted on it. Simeon, [its stone was] a peridot, its banner was dyed green, and Shekhem was depicted on it. Levi, [its stone was] an emerald, its banner was dyed one-third white, one-third black, and one-third red, and the urim and tumim were depicted on it.
Judah, [its stone was] a turquoise, the color of its banner was in its image, like the heavens, and a lion was depicted on it. Issachar, [its stone was] a sapphire, its banner was dyed bluish-black, and the sun and the moon were depicted on it, based on: “From the children of Issachar, possessors of understanding of the times” (I Chronicles 12:33). Zebulun, [its stone was] a clear quartz, the color of its banner, white, and a ship was depicted on it, based on: “Zebulun will dwell at the seashore, [and he shall be a shore for ships]” (Genesis 49:13).
Dan, [its stone was] a jacinth, the color of its banner was like a sapphire, and a serpent was depicted on it, based on: “Dan will be a serpent” (Genesis 49:17). Gad, [its stone was] an agate, and the color of its banner was neither white nor black, but rather white and black intermingled, and an encampment was depicted on it, based on: “Gad will wage war by regiment” (Genesis 49:19). Naphtali, [its stone was] an amethyst, the color of its banner was similar to clear wine whose redness is not deep, and a hind was depicted on it, based on: “Naphtali is a hind let loose” (Genesis 49:21).
Asher, [its stone was] a beryl, and the color of its banner was like the gem with which women adorn themselves, and an olive tree was depicted on it, based on: “From Asher, his bread is rich [shemena]” (Genesis 49:20). Joseph, [its stone was] onyx, the color of its banner was exceedingly black, and it was depicted for two princes, Ephraim and Manasseh: Egypt, because they were born in Egypt. On the banner of Ephraim an ox was depicted, based on: “The firstborn of his bull [is his majesty]” (Deuteronomy 33:17); this is Joshua bin Nun, who was from the tribe of Ephraim. On the banner of Manasseh, an aurochs, based on: “And his horns are the horns of an aurochs” (Deuteronomy 33:17); this is Gideon son of Yoash, who was from the tribe of Manasseh. Benjamin, [its stone was] a chalcedony, the color of his banner was like all the colors of the twelve colors, and a wolf was depicted on it, based on: “Benjamin is a mauling wolf” (Genesis 49:27). That is why it is stated: “With the insignias,” as each and every prince had his own sign.

“he brought me to the banquet house,” when the Holy One blessed be He appeared upon Mount Sinai, twenty-two myriads of angels descended with him, as it is stated: “The chariots of God are myriad, thousands upon thousands of companies” (Psalms 68:18), and they were all arranged according to banners, as it is stated: “Preeminent [dagul] among a myriad” (Song of Songs 5:10). When Israel saw that they were all arranged according to banners, they began desiring banners. If only we could be arranged according to banners like them. Therefore, it is stated: “He brought me to the banquet house, [and his banner of love is upon me],” this is Sinai, at which the Torah, which is likened to wine, was given.

שכן לשבטיו DWELLING ACCORDING TO HIS TRIBES — He saw each tribe dwelling by itself not intermingled one with another; he saw that the entrances of their tents were not exactly facing each other so that one could not peer into the other's tent (Bava Batra 60a).

How fair are your tents, O Jacob,Your dwellings, O Israel!