(a) RASHI (DH Ma'aleh Alav ha'Kasuv) explains that by eating and drinking the day before one prepares himself for the fast. Since his eating and drinking on the ninth is in *preparation* for the fast of the tenth, his eating is considered to be a part of his later fasting. This is also the opinion of the ROSH (Yoma 8:22), and support can be found for it in the Yerushalmi (Yoma).

(b) The SHIBOLEI HA'LEKET, quoting RABBEINU YESHAYA, says that after eating and drinking a lot on the day before the fast, fasting is much more difficult. Therefore one is rewarded for eating on the ninth as if he has lengthened his fast of the tenth. (Support for this understanding can be drawn from the Gemara in Ta'anis 26a, which says that fast-days are not established on Sundays, for it is too hard to fast after a day of festivity -- Pardes Yosef, Vayikra)

The ARUCH LA'NER (Rosh Hashanah 9a) suggests a novel approach. During the year, a person sins with his body and with his soul. By fasting on Yom Kipur, one afflicts his body. By eating on the day before Yom Kipur, one afflicts his soul, which is weakened by physical pleasures.

(a) The TUR (Orach Chayim 604) quotes the Midrash that tells the story of a simple Jew who outbid the king's officer to buy a fish on the day before Yom Kipur. The Jew later explained to the king that he wanted the fish "to celebrate that Hashem was going to pardon the sins of the Jewish people" the next day. From this it can be learned that eating on the day before Yom Kipur shows one's faith that the fast of the following day will earn us a complete pardon. RABBEINU YONAH (Sha'arei Teshuvah 4:8) also suggests such an explanation.

(b) Since Yom Kipur is a Yom Tov, it requires a Se'udas Yom Tov, a festive meal. However, we cannot have a Se'udah on Yom Kipur because we are commanded to fast. The Se'udah, therefore, was moved to the ninth. Since the Se'udah of the ninth is part of the celebration of the tenth, by eating on the ninth it is considered as if one fasted on both the ninth and the tenth. (Rabbeinu Yonah, Sha'arei Teshuvah 4:9)

All of these reasons assume that eating on the ninth of Tishrei is related to the fast and atonement of the tenth of Tishrei, Yom Kipur. Consequently, it may be concluded that women are also obligated to eat on the ninth of Tishrei, even though it is a time-dependent obligation from which women are normally exempt. Since women must fast on Yom Kipur, they are also required to do everything connected with that fast, including eating on the ninth. This is how the MAHARIL rules as cited by the DARCHEI MOSHE, Orach Chayim 604:1.