Chazal tell us that one who eats on Erev Yom Kippur gets credit as if he fasted two days. Mar, son of Ravina, would fast all year except for three days: Purim, Shavuos, and Erev Yom Kippur (Pesachim 68).
Tosfos (Rosh HaShana 9b) asks: the gemara tells us that even though R' Eliezer and R' Yehoshua disagree whether eating a meal is required on a regular Yom Tov, whether "chatzi lachem" is required to balance out the "chatzi laHashem", they both agree that on Shabbos, Shavuos, and Purim eating is required. Why does the gemara not also say that they both also agree that eating on Erev Yom Kippur is required?
R' Tzadok HaKohen answers (Pri Tzadik Erev Y"K 4) that there is a conceptual difference between the eating required on erev Yom Kippur and the eating required on Yom Tov. Eating on Shabbos or Yom Tov is done to fulfill the requirement of "lachem" or "oneg", to physically enjoy the day. The purpose of eating on erev Yom Kippur is not for the sake of "lachem" -- it is not for our own physical enjoyment, but rather must be done purely l'shem shamayim.
The requirement to eat on erev Yom Kippur is derived from the same source as the requirement to fast on Yom Kippur, "v'inisem es nafshoseichem". Why nafshoseichem in the plural? We face a dual challenge: to avoid the temptation for indulgence that entices our lower, base instinct/soul, and to be proper consumers of the world as required to energize our positive faculties/soul. The former is the lesson we learn from withdrawal from the world on Yom Kippur; the latter is the lesson of the meal on erev Yom Kippur.