This day also begins the count toward the Feast of Weeks שבועות. Shavuot. This marks the beginning of the latter fruits, the wheat harvest. In Christian tradition, the 50th day, the Holy Spirit was given. This day, called "Pentecost" in the Greek, is also the Biblical Holiday: Shavuot ("weeks"). (see Leviticus 23:15-16 and Acts 2) In fact, it was because of this Festival and the requirement to be in Jerusalem, that there were so many Jews there to witness the "giving of the Holy Spirit".
Christian John Parsons examines this day of First Fruits and how it relates to all the Spring Festivals in greater detail --> here.
Messianic Jew Ron Cantor explains the different counting and why --> here
Chabad.org explains the Judaic tradition today --> here
Judiasm 101 has more links and information --> here