In the previous Mishnah we learned that a person completes the order of the Seder right up to the washing of the hands for matzah and maror, and afterwards the meal is eaten. Our Mishnah opens with a description of what takes place after the meal.
The Third Cup:
A third cup is poured for him, and over it he recites Birkas HaMazon.
The Fourth Cup:
Over the fourth cup he completes the rest of Hallel, and recites over it what is called "Birkas HaShir" - the blessing of the song. What is this Birkas HaShir?
Some explain that this is the berachah that concludes Hallel, which ends with "Yehalelucha."
Others say that it refers to "Nishmas," which likewise concludes with "Yishtabach."
We also mentioned that the Gemara explains that we add what we call "Hallel HaGadol," and with that we conclude.
Drinking Between the Cups:
"Bein hakosos ha'eilu" - between these cups, that is, between the first two cups and the last two, if he wished to drink, he is permitted to do so, since wine drunk in the middle of the meal does not intoxicate.
Between the third cup and the fourth - one may not drink, out of concern that he will become intoxicated and be unable to complete the Seder.
Wine before the meal - its status is like that of wine during the meal, and it too does not intoxicate. Therefore it is also permitted to drink between the first cup and the second.
In summary: In this Mishnah we learned the order of the last two cups: over the third cup Birkas HaMazon is recited, and over the fourth Hallel is completed and Birkas HaShir is said - whether according to the opinion that it is "Yehalelucha" or the opinion that it is "Nishmas," which concludes with "Yishtabach" - and with the Gemara's addition we conclude with Hallel HaGadol. We also learned the laws of drinking between the cups: it is permitted before the meal and during it, and forbidden between the third cup and the fourth out of concern for intoxication that would prevent the completion of the Seder.