Isru Chag (אסרו חג, lit. 'Bind [the] Festival') refers to the day after each of the Three Pilgrimage Festivals. The phrase originates from Psalms 118:27, which states, "Bind the festival offering with cords to the corners of the altar." According to the sages of the Talmud, this verse homiletically means, "Whosoever makes an addition to the Festival by eating and drinking is regarded by Scripture as though he had built an altar and offered thereon a sacrifice."
In response to a community inquiry about the significance of Isru Chag, Rabbi Yosef Hayyim (1832–1909), known as the Ben Ish Chai, referenced the Arizal (1534–1572), the architect of Lurianic Kabbalah. He explained that Jews connect the day after the holiday to the holiday itself because of the residual "light" of the holiday. This additional day of celebration is intended to extend the sanctity of the holiday.
Adding a degree of festivity to the day as a practice has further been codified in Ashkenazic communities, as Rema, Rav Moses Isserles (1520–1572) has stated in his glosses on the Shulchan Aruch in the section Orach Chayim:
And we have the custom to eat and drink a little more on the day after the holiday – and that is the day known as "bind the festival." (— Orach Chaim 429:2)
The Chofetz Chaim, Harav, Yisrael Meir Kagan (1838–1933) ruled that the minhag (custom) is to generally forbid fasting on Isru Chag, except in instances when, as a result of great distress, the community synagogue decrees it. [Mishna Berurah Orach Chaim 429:14]
Almost all communities omit tachanun on Isru Chag. However, communities that follow the rulings of Maimonides (1135–1204) maintain that the only days on which Tachanun is to be omitted are Shabbas, MOadim, Rosh HaShanah, Rosh Chodesh, Chanukkah, Purim, and the mincha on the eve of any Shabbas and holiday. [Mishnah Torah, Hilchos Tefillah 5:15]