It is a mitzvah to eat and drink heartily on Erev Yom Kippur. Our Sages write: The Torah (Leviticus 23:32) states: And you shall afflict your soul on the ninth of the month in the evening.
Do we fast on the ninth? We fast only on the tenth! [How then is this verse to be understood?] It comes to teach us that all who eat and drink on the ninth, and fast on the tenth, are considered by Scripture as if they had fasted on both the ninth and the tenth.
The reason why eating on the ninth is considered so great a deed that it is equivalent to having fasted, is that by doing so, we show our joy that the time for our atonement has arrived. By extension we thus show that we are concerned with our sins.
Another reason: On other Festivals we partake of fixed meals as a means of expressing our happiness in having the opportunity to fulfill mitzvot. This joy is in itself a source of merit. Since we cannot partake of a festival meal on Yom Kippur, we do so on the day before Yom Kippur instead.
A third reason: The festive meal on Erev Yom Kippur provides us with the physical strength needed on Yom Kippur to focus ourselves on prayer, supplication, and reflection that will lead us to teshuvah.
Tur (Orach Chayim 604) states:
This (eating on Erev Yom Kippur) stems from His great love for His people, for He commanded them to fast only one day a year - for their benefit, so that their sins might be atoned. He commanded them to first eat and drink so that they might fast and the affliction would not harm them.
It is customary to eat fish at the morning meal on Erev Yom Kippur.
The Midrash (Bereshit Rabbah 11) recounts:
R. Tanchuma taught: It once happened in Rome on Erev Yom Kippur that a Jewish tailor went to the market to buy fish. There was only one fish available, but there were two buyers: the tailor and the servant of the Roman governor. Each offered a progressively larger sum until the price reached twelve dinar, which the tailor paid.
During the governor's meal, he asked his servant: "Why did you not bring ash?" The servant replied: "I shall not hide the truth from my master. I went to buy fish, but there was only one available. A Jew and I haggled over it- each of us offering more than the other- until the price reached twelve dinar. Would you have wanted me to spend twelve dinar on a fish?" The governor asked: "Who is this Jew?"
He sent for him and he was brought before him. He asked him: "Why did you, a Jewish tailor, see fit to eat a fish that cost twelve dinar?" The tailor replied: "Sir! We have but one day during which all the sins that we commit throughout the year are atoned for. Shall we not honor that day when it comes?" The governor replied: "Since you have explained your behavior, you may go."
And how did G‑d repay the tailor? When he opened the fish, G‑d summoned a precious jewel [into the fish] and this provided him with sustenance for all his days.
Although it is a great mitzvah to eat heartily on Erev Yom Kippur, one should be careful to eat only those foods that are easy to digest. We find that some righteous tzaddikim who never gorge themselves the rest of the year - would partake of many light meals throughout the day so as to derive joy in the mitzvah that accompanies each bite of food.