Rashi: Because that is when one harvests the new wheat-crop. ¹

Rashbam: Because on Shevu'os one brings the Korbanos mentioned in Emor, 23:17-20, including the Sh'tei ha'Lechem, which are the first Minchah to be brought from Chadash - the new crops.

Chagigah, 18a #1 (citing Resh Lakish): We learn from here that the Korban Chagigah may be brought on the six days after Shevu'os ('Shiv'as Yemei Tashlumin'), wwhen harvesting is permitted.

Chagigah, 18a #2 (citing R. Yochanan: The Torah means the Yom-Tov ¹ that falls during the harvest season. ²

Yerushalmi Chagigah, 2:4: The current Pasuk is speaking about Yom-Tov that falls during the week, when one brings tha Chagigah but does not rep the harvest, whereas the Pasuk in Emor, which is discussing Yom-Tov that falls on Shabbos, when one brings the Chagigah on Sunday and also harvests then.

Rashi and Rashbam: It refers to the Sh'tei ha'Lechem - the first Korban that one brings to the Beis-Hamikdash on Shavu'os from the current year's wheat-harvest, together with the accompanying set of Korbanos. ¹ which permit Chadash in the Beis-ha'Mikdash.

Bikurim, 1:3: It implies that one may may not bring Bikurim before (one has brought the Sh'tei ha'Lechem on) Shevu'os. ¹

Menachos, 84b: Based on the Gezeirah Shavah "Ma'asecha" "Ma'asecha" - in the same Pasuk, in connection with the Nesachim and fruit of the tree, it implies that the Sh'tei ha'Lechem (which are also called 'Bikurim') precede the Nesachim and permission to eat the new fruit. ²

Menachos, 71a: To teach us that seeds that have taken root before the Omer become permitted when it is brought. ¹

Menachos, 84b: It teaches us that the Sh'tei ha'Lechem on Shavu'os precede, not only the first-fruits of wheat, ² but also of barley. ³ And the Torah adds "ba'Sadeh" to incorporate seeds which were not planted, but which grew by themselves in the Halacha.

Rashi: Because throughout the summer, the produce is left out in the field to dry, and it is at Succos-time that it is taken into the house before the rain season begins.

Rashbam: Because we sit in the Sukah when the produce is gathered from the field to fill the granaries and wine and olive-presses - to remind us of the time in the desert, when we lived in tents (huts) when we did not possess land, grain, wine or oil, and to thank Hashem for the fact that we have them now.

Rosh Hashanah, 13a: Bearing in mind the continuation of the Pasuk "be'Osp'cha es Ma'asecha ... ", the Torah is teaching us that what is harvested ¹ on Sukos goes after the previous year ² (when they have grown one third of their full growth).

Chagigah, 18a: The Pasuk is merely referring to the Yom-Tov that falls during the ingathering season. ³

Seforno: It means after the ingathering of the previous year's produce has been concluded.

Yerushalmi Rosh Hashanah, 1:2: In conjunction with the Pasuk in Ki Sisa, 34:22 've'Chag ha'Asif be'Tzeis ha'Shanah", the Yerushalmi extrapolates from the fact that the only month that contains a Chag, a new Tekufah, Asif and the end of the year is Tishri, and that consequently, we reckon the years from Tishri. ¹

Ramban: With reference to the Pasuk "Shalosh Pe'amim ba'Shanah ... (in Pasuk 14), The Torah continues that the three Regalim should coincide with the beginning of the spring (Pesach), with when the first crops are harvested (Shavu'os) and with the in-gathering of the harvest (Sukos).

Ramban #1, Targum Onkelos and Targum Yonasan: In means 'before the Master, Hashem'.

Ramban #2 (according to Kabalah): Refer to 20:3:4:4*.

Ramban and Seforno: The Torah connects the Regalim with the stages of the harvesting of the crops, to teach us that one of the functions of the Yamim-Tovim and one of the reasons for Aliyas ha'Regel to visit the Beis-Hamikdash on those three occasions, is to thank Hashem, the Master of the World, for his kindness in providing us with the seasonal blessings - each one in its time. ¹

Rashbam: Hashem is Master of the land - and He will ensure that nobody will covet it and steal it when you leave it to fulfil the Mitzvah of Aliyas ha'Regel. ²