They poured for the leader of the seder the third cup of wine, and he recites the blessing over his food, Grace After Meals. Next, they pour him the fourth cup. He completes hallel over it, as he already recited the first part of hallel before the meal. And he also recites the blessing of the song at the end of hallel over the fourth cup. During the period between these cups, i.e., the first three cups established by the Sages, if one wishes to drink more he may drink; however, between the third cup and the fourth cup one should not drink.

One does not conclude after the Paschal lamb with an afikoman. If some of the participants at the seder fell asleep, thereby interrupting their meal, they may eat from the Paschal lamb when they awake. If the entire company fell asleep, they may not eat any more. If they all fall asleep, this is considered a complete interruption, and if they were to resume their meal it would be akin to eating the offering in two different places. Rabbi Yosei says: If they dozed they may eat from the Paschal lamb when they awake, but if they fell fast asleep they may not eat from it.

GEMARA: The Gemara asks: What is the meaning of afikoman? Rav said: It means that a member of a group that ate the Paschal lamb together should not leave that group to join another group. One who joined one group for the Paschal lamb may not leave and take food with him. According to this interpretation, afikoman is derived from the phrase afiku mani, take out the vessels. The reason for this prohibition is that people might remove the Paschal lamb to another location after they had begun to eat it elsewhere. This is prohibited, as the Paschal lamb must be eaten in a single location by one group.

And Shmuel said: It means that one may not eat dessert after the meal, like mushrooms [urdila’ei] for me, and chicks for Abba, Rav. It was customary for them to eat delicacies after the meal. And Rav Ḥanina bar Sheila and Rabbi Yoḥanan say: Afikoman refers to foods such as dates, roasted grains, and nuts, which are eaten during the meal. It was taught in a baraita in accordance with the opinion of Rabbi Yoḥanan: One does not conclude by eating after the Paschal lamb foods such as dates, roasted grains, and nuts. Rav Yehuda said that Shmuel said an additional halakha: Nowadays, when we have no Paschal lamb, one does not conclude after matza with an afikoman. The Gemara asks: We learned in the mishna that one does not conclude after the Paschal lamb with an afikoman. The Gemara infers from the mishna: It is after the Paschal lamb that one may not conclude with an afikoman; however, after matza one may conclude with an afikoman. This statement of the mishna apparently contradicts Shmuel’s ruling.

The Gemara rejects this contention: That is an incorrect inference, as the mishna is stated in the style of: Needless to say. The mishna should be understood as follows: Needless to say that one may not conclude with an afikoman after eating matza, as the taste of matza is slight. If one eats anything else afterward, the taste of the matza will dissipate. However, after the Paschal lamb, which has a strong taste that is not easily removed, one might think that we have no problem with it. Therefore, the mishna teaches us that it is prohibited to conclude with an afikoman after the Paschal lamb as well.

מפטירין – I heard the language of (Psalms 22:8): “[All who see me mock me;] they curl their lips, [they shake their head],” that is to say, they open and say, and my teachers/Rabbis explained the language of taking leave from his friend, for when they leave from the meal, they should not conclude it with the Afikomen, “to take out from before you,” that is to say, remove your utensils from here and let us go and eat in another place, neither bread nor anything, and this was decreed lest one comes to eat the Passover sacrifice in two places, but it is permitted to eat other things in his first place, as long as he does not uproot himself from this group to eat them with another group. And there is in the Gemara (Pesahim 119b) one who explains that “After the Passover meal, we don’t conclude with the Afikoman,” to mean that we don’t take out types of sweet things, and after they have eaten the Passover sacrifice, they should not conclude the meal with the eating of sweet things and fruits that are regularly eaten as a desert, and even in their [own] place, so that they don’t lose the taste of the Passover [sacrifice] from their lips. And this is the most important thing. But just as we don’t conclude the meal after the Passover offering with an Afikoman, we don’t conclude after eating Matzah with an Afikoman, for they would need to eat an olive’s bulk of Matzah at the end at the time when there is no Passover sacrifice, and after that Matzah, we don’t conclude that meal with the eating of another thing.

... Such as truffles for me, and chicks for Abba. For Rav (Abba is Rav). As Shmuel was accustomed to eating truffles and mushrooms as a dessert and Rav was accustomed to eating chicks after his meal. the language used, afikoman, means "take out and bring sweet thing." And Shmuel was coming to say that one doesn't need to say that one shouldn't move from one group to another, but even in one's own group it is forbidden to eat anything after the Paschal sacrifice, so that one doesn't lose the taste of the meal. And since the law is to eat it at the end when satiated, as is the case with all sacrifices as it says (Numbers 18) "The gifts are given as a mark of greatness" and should be eaten in a manner that kings eat.

(Translation from Hadran.org.il)