We continue with Maseches Menachos, chapter 10, mishnah 6. In the previous mishnah we learned that once the Omer offering has been brought, the new year's grain becomes permitted for human consumption. Now the mishnah teaches that there is an additional date relating to the new crop of wheat and barley, distinct from the permission of the new grain that follows the bringing of the Omer: even though one may eat from the new grain after the Omer has been brought, one may not bring menachos from this year's crop until after the waving of the Two Loaves on Shavuos, close to seven weeks later.
The reason is that the verse refers to the Two Loaves as a "minchah chadashah" - a new meal offering. And what makes it new? The fact that it comes from the new grain. From here we learn that one may not bring meal offerings from the new grain before the new meal offering, that is, before the Two Loaves. This, then, is a second deadline.
The source for the disqualification before the Omer:
There is a derivation from a verse in Yechezkel that refers to "mimashkeh Yisrael." The exposition is that food which is not permitted, that a Jew may not eat, cannot be offered on the altar. What this means is: before the Omer is brought, since wheat and barley are forbidden for human consumption, they are also forbidden to be offered on the altar - and therefore, as the mishnah will state, the offering is invalid even after the fact.
The matter of "minchah chadashah," however - that the first offering to use the new grain of the year should specifically be the Two Loaves - is only a requirement ideally. After the fact, if an offering from the new grain was already brought after the Omer but before the waving of the Two Loaves, it is valid. This is the foundation of the mishnah's words.
The words of the mishnah:
"HaOmer hayah matir bamedinah, ushtei halechem bamikdash" - we have before us two permitting factors, two mechanisms through which the new year's grain becomes permitted:
"HaOmer hayah matir bamedinah" - outside the Beis HaMikdash, meaning for human consumption, the permitting factor is the Omer offering.
"Ushtei halechem bamikdash" - what permits the use of the new year's grain for menachos is the waving of the Two Loaves. The two loaves of bread are not placed on the altar, since they are chametz, but rather are waved.
"Ein mevi'in menachos uvikkurim uminchas beheimah kodem la'Omer" - before the Omer is brought, these three may not be brought from this year's grain:
Menachos - a meal offering that comes from this year's wheat or barley.
Bikkurim - the first fruits, which come from all seven species with which Eretz Yisrael is praised: wheat and barley, and also olives, dates, grapes, figs and pomegranates. Our mishnah is speaking of the first two, wheat and barley, which may not be brought before the Omer even after the fact.
Minchas beheimah - these are the meal offerings of the libations that accompany every olah and every shelamim, which may not be brought before the harvesting of the Omer.
"Ve'im heivi - pasul" - even after the fact the offering is not valid. It follows that if one placed the meal offering in a service vessel, as one is required to do before bringing a meal offering, the vessel sanctifies it with inherent sanctity, and nevertheless it may not be offered. Once it is disqualified even after the fact, nothing further can be done with it: it becomes disqualified by being left overnight, and in the end it must be burned.
"Kodem lishtei halechem lo yavi, ve'im heivi - kasher" - before the Two Loaves as well, one may not bring, ideally, menachos from this year's wheat or barley, nor bikkurim of wheat and barley, nor the libations of the offerings. But if one did bring them, they are valid after the fact, because the requirement of "minchah chadashah" is not an indispensable requirement.
Therefore, if in the end a person did bring the meal offering up onto the altar and even burned it, and sanctity has already taken hold of it - we do not disqualify it. The offering is valid after the fact, and once it has been done, it has been done, and there is no need to bring another in its place. This rule applies both to meal offerings and to bikkurim: one who brings bikkurim or a meal offering before the Omer has been brought is obligated to bring others in their place; but one who brings after the Omer and before the Two Loaves, even though he should not do so at the outset, has fulfilled his obligation with regard to all the laws of after the fact.
Summary: In this mishnah we learned about two permitting factors for the new grain - the Omer, which permits the new grain "in the country" for human consumption, and the Two Loaves, which permit the new grain "in the Temple" for bringing meal offerings, by virtue of their being a "new meal offering." Before the Omer one may not bring meal offerings, bikkurim, or the meal offering that accompanies an animal offering, and if one did bring them, they are invalid even after the fact, based on the exposition of "mimashkeh Yisrael" - that whatever is not fit for a Jew to eat is not offered on the altar. Before the Two Loaves, the prohibition is only at the outset, and if one did bring, it is valid.