Chag Habikurim is the least well-known of the names of Shavuot (after Chag Hacheesecake etc). It refers to the offering of the first fruits that farmers in the Land of Israel brought to the Temple in Jerusalem in early summer at around the time of the Shavuot holiday. The word bikurim itself is related to bechor, a firstborn son.
The finest of the first-ripening fruits would be brought with great ceremony in ornate baskets to the Temple. The Bible describes a strange ritual that would then take place (Deuteronomy 26:1-11).
The bringer of first fruits recited the vidui bikurim, a lengthy declaration describing how he came to be there. Beginning with "My father was a wandering Aramean," he goes on to recount how the Jewish people were enslaved in Egypt, how they cried out to God who saved them, took them out of Egypt and brought them to the Land of Israel - the best of whose fruits he is now bringing to the Temple.
The farmer tells a story to account for his good fortune that stretches back to the beginnings of the Jewish people. Full gratitude comes from understanding the roots of his present situation. As the Sefer Hachinuch (a medieval compendium of the 613 mitzvot) says, the reason for the declaration is to etch on our hearts the reality of God's kindness.