Why do we observe Shavuot by studying all night?

Answered by
George Robinson

Since the Rabbinic period, Shavuot has been tied to the story of receiving the Torah. Connected to this, Shavuot has come to be dedicated to the idea of Torah study and Jewish education. One custom is an all-night [or late night] study session held on the first evening of the festival, called tikkun leil Shavuot. This custom, which had its beginning in the community of kabbalists centered around sixteenth-century Safed, is designed to prepare Jews for “receiving” the Torah again on Shavuot.

See also: 
What is a Confirmation?
Tikkun Leil Shavuot Videos and Study Guides