Shavuot this year (5776, 2016) begins at the end of Shabbat June 11. In Israel it ends Sunday night, outside of Israel it ends Monday night.
Shavuot as a Universal Holiday
There are 620 letters in the Ten Commandments, corresponding to the 613 mitzvot of the Torah and the additional 7 mizvot of Bnei Noach. The Torah cannot be given to Israel unless it has at least one universal branch. Jethro, the father-in-law of Moses, came in the name of all of humanity to participate in the momentous event of the giving of the Torah. G-d offered the Torah to the other nations, but most of the people rejected it. But, as the Polish Count Pototzky said, "Today it is possible to be a Ben Noach and to accept the Torah." This means that the holiday of receiving the Torah is not just for the Jews but is a celebration for the entire world.
Shavuot and the First Fruits
The significance of Bikurim - giving away the first fruits:
It is not explicitly written that the Torah was given on Shavuot, but the Torah does give the holiday as the date for Bikurim - bringing the first fruits to the Temple. Any man who has labored for an entire year definitely wants to eat the first fruit, but he gives it to somebody else - to a priest in the holy Temple. This act reminds of King David, who was born and died on Shavuot. David wrote the Five Books of the Psalms as prayer and praise of G-d in response to the Five Books of the Torah, which are the Word of G-d brought down from heaven to mankind.