Fifty days after Firstfruits — the wheat harvest, and the day the church began.
Seven weeks and a day are counted from the wave sheaf, which is where both names come from: Weeks in Hebrew, and Pentecost in Greek, meaning fiftieth. It is a harvest feast — two loaves of the new wheat, baked with leaven this time — and one of the three at which every man was to appear. It is the feast Jerusalem was full of pilgrims for when the Spirit came, which is why the crowd in Acts 2 is listed by the countries it came from.