The day after a Yomtov is known as Isru Chag. In Israel it is another day for the holiday atmosphere to linger, another day off from school and nursery and another excuse for government offices to not quite return to normal functioning.
The Jewish-words blog, balashon, has an interesting exploration of Isru Chag, to which I am indebted. The phrase occurs in Psalm 118:27 (part of Hallel): Bind the holiday offering (Isru Chag) to the horns of the altar with cords.
In its plain meaning, it is a request from pilgrims visiting the Temple to the priests.
The Talmud in Succah 45a offers a number of interpretations of this verse. One states says that anyone who binds the lulav with the hadas (myrtle) is as if he built an altar and brought a sacrifice Another states that anyone who makes an isur for the chag (festival) with food and drink is as if he built an altar and brought a sacrifice.
The phrase to make an isur for the chag is obscure.The first of Rashis two explanations is one who makes a (social) bond for the chag, ie who brings people together to celebrate the holiday. This plays on the word isur which means to bind, tie up or encircle. Rashis second explanation is that there are those that say the day after the chag ie we bind an extra day of celebration to the end of the holiday.
Rabbi Moshe Isserles (Orach Chaim 429:2) quotes this second opinion in Rashi, and from here we have the custom to eat and drink a bit more on the day after a holiday.