In this week's Parsha, we learn about the falling of the מן to provide the people with food in the desert. The Torah teaches us that although the מן fell daily, it did not fall on Shabbos, and instead a double portion fell on Friday. A question arises about Yom Tov. Did the מן fall on Yom Tov or did it not? If it did not, we must assume that a double portion fell on Erev Yom Tov. Did this happen?
There are two opinions in the Midrash regarding this question. The first Midrash comments on a Posuk in Parshas Bereishis which says "ויברך אלוקים את יום השביעי ויקדש אותו," meaning that Hashem blessed the seventh day and made it holy )בראשית ב':ג'(. Rashi explains that Posuk as teaching that Hashem blessed Shabbos through the מן, and He also sanctified the Shabbos in connection with the מן. Actually, He blessed the whole week by providing daily מן, but this blessing did not apply to Shabbos. By distinguishing the day of Shabbos in this manner, He sanctified the day. The day was blessed too, though, because the מן that had fallen on the previous day was still edible, and that didn't happen on any other day. Since, however, the Posuk indicates that only Shabbos was blessed and sanctified by means of the מן, we can learn that Yom Tov was not similarly distinguished, and thus we may conclude that the מן must have fallen on Yom Tov.
Another Midrash, however, comments on the Pesukim in our Parsha and states that the מן did not fall on Yomim Tovim either. A double portion fell instead on Erev Yom Tov, just as it did on Erev Shabbos. These two Midrashim are mentioned in Tosafos in Beitzah )דף ב: בד"ה והיה( where we find an interesting view that even those who hold that מן generally did fall on Yom Tov agree that if Yom Tov landed on Friday, it did not fall because, due to Yom Tov, it would not have been possible to prepare it for Shabbos anyway.
There are two ramifications of this dispute between the Midrashim about מן on Yom Tov. The first deals with the Mitzvah of Lechem Mishneh, having two loaves of bread at each Shabbos meal, which is a remembrance of the fact that a double portion of מן fell on Erev Shabbos. Whether one requires Lechem Mishneh on Yom Tov too depends on our question. The view that holds that מן did not fall on Yom Tov must hold that a double portion fell on Erev Yom Tov, and thus Lechem Mishneh is needed for Yom Tov too. The view that holds that מן did fall on Yom Tov would hold that no Lechem Mishneh is needed for Yom Tov because there was no double portion to commemorate.
A second ramification relates to how to interpret the Posuk which states אל יצא איש ממקומו ביום השביעי, meaning that one should not leave one's place on Shabbos )שמות ט"ז:כ"ט(. The view that holds that מן did fall on Yom Tov, and only on Shabbos did it not fall, may believe that it did not fall on Shabbos because of the prohibition of carrying. On Yom Tov, when carrying is permitted, the מן certainly could and did fall. This Posuk would then be coming to restrict one from carrying from one's place on Shabbos, not from leaving. It would then have no application to Yom Tov, when carrying is allowed, and the מן was indeed carried. The other view, however, holds that the Posuk has nothing to do with carrying, because the מן did not fall on Yom Tov either, despite the permissibility of carrying. Rather, the Posuk is coming to teach the law of Techum Shabbos, which limits how far a person may walk beyond a populated area on Shabbos. This law applies to Yom Tov as well. The Posuk teaches that the people could not walk a certain distance on Shabbos which they usually did to collect their מן; since no מן fell, there was no need to take this walk. Since no מן fell on Yom Tov either, this prohibition appilies to Yom Tov as well.