The Mishna on our daf concludes the discussion of the seder with the last two of the four cups. The Mishna teaches that the third cup accompanies the grace after meals, and the fourth cup accompanies the completion of Hallel. The Mishna also teaches that no other wine can be drunk between these last two cups.
The Jerusalem Talmud explains the prohibition against drinking between these cups of wine as stemming from a concern lest the participants in the seder become drunk, for drinking before the meal or during the meal is not as intoxicating as wine drunk after the meal without any other food. The Ge’onim simply explain that this is connected to the general prohibition against eating anything after the afikoman – the last matza eaten at the end of the seder – aside from what is expressly commanded by the Sages. The Ra’avad argues that drinking more wine toward the end of the seder would have the effect of hiding the unique four cups that we drink on this night. In order to emphasize the celebration of the miracle of the Exodus through these four cups (see Pesahim 99), we cannot add to them.
It is interesting to note that there are variant readings of this Mishna, one of which suggests that there is a fifth cup on which Hallel ha-Gadol (see full explanation on daf 118) is recited. This was, apparently, the version of the Mishna that appeared before the Rif and Rabbenu Hananel, who rule that there is a mitzva to drink a fifth cup, as well. Even the Rambam, who rules that there is no obligation to drink a fifth cup, allows one to do so.
It appears that this disagreement is the source for our Kos shel Eliyahu, which is poured towards the end of the seder, but is not drunk. Tradition has it that it is left for the prophet Eliyahu who visits every Jewish home on the seder night, foreshadowing the ultimate redemption..