First Fruits celebrates the beginning of the grain harvest, at that time of year the first of the barley. For information about the presenting of the "first fruits" portion of produce at the Temple, please refer to our vocabulary page about tithing.
It happens during Pesach, and in much of Rabbinical Judaism is ignored because it became culturally "overwhelmed" by its proximity with Pesach.
The holiday was important while the Temple stood. Thus the Apostles make use of the imagery of First Fruits:
In Leviticus 23:15-16 we read about a "day after the Shabbat" that is elsewhere named First Fruits (HaBeekooreem).
When is this day? This is a tricky question. In Leviticus 23:15-16 we read about a time soon after Pesach:
From the day after the Shabbat, the day you brought the sheaf of the wave offering [First Fruits], count off seven full weeks, until the day after the seventh week. Count off fifty days, and then present an offering of new grain to Adonai.
There is disagreement on which Shabbat is referred to in the beginning of those verses. Is it the usual weekly day of rest that falls during the seven days of Pesach? Or is it the first day of Pesach, which is another day of rest?
In First Century Judaism, the Sadducees believed the former answer was correct, and the Pharisees believed the latter answer was correct. Rabbinical Judaism accepts the latter since it came from the Pharisees. But most people in Messianic Judaism believe that the former answer is correct.
The Sadducees asked, "If the appointed time is always the 15th day of Nissan then why wouldn't the Torah simply say so?"
The Pharisees asked, "What other holiday has a fixed day of the week instead of a fixed day of the month?"
(Historians cannot even agree upon which dating system was in use in Acts 2:1. The Sadducees controlled the Temple activity, but the Pharisees had greater influence socially. Which sect controlled the calendar in those days is debated.)
Why does the disagreement make a difference? First Fruits as celebrated by Rabbinical Judaism may fall on any day of the week. But First Fruits as celebrated by most of Messianic Judaism always falls on a Sunday (as does Shavuot). This emphasizes that First Fruits is a foreshadowing of Yeshua's day of resurrection.
Many people enjoy a sunrise service to celebrate the resurrection. This is appropriate, but can be tricky to do in a Jewish way culturally distinct from an "Easter service" (even though it may fall on the same day).
Acts of encouragement are also appropriate, since this is a day that commemorates how God takes care of us!