Can anyone tell me the meaning of the first fruits as related to the Fall festivals in the Tenauch !!!?

Answer 1

You are referring to "bikkurim", which translates as "first fruits". And it's "Tanakh", not "Tenauch", just fyi.

The offerings of first fruits were both an individual obligation and a part of public festival celebrations, particularly the celebration of Shavuot, also called Hag ha-Bikkurim, “the first fruits festival” (Ex. 23:16; 34:22; Lev. 23:16–17; Num. 28:26).

A sheaf of the new barley harvest ('omer) was offered on the second day of the Passover festival (Lev. 23:10–11, 15–16). According to the Mishnah (Bik. 1:3,6,9), in Second Temple times the pilgrimage to the Temple for the purpose of offering the first fruits could be undertaken anytime between Shavuot, in the late spring, and Sukkot, in the fall (but see below), but the festival of Shavuot was the first date for this offering.

Answer 2

http://www.cog21.org/holydays.html

http://www.pcog.org/Default.asp?sitemapId=LiteratureQuip&LitList=19&id=1247

http://www.cbcg.org/Calendar/index.html