Shavuot is a holiday which celebrates the giving of the Torah at Mount Sinai. It also commemorates the time when the first fruits were harvested and brought to the Temple.
One of the customs for the holiday is to eat dairy meals. A few reasons are given for this, but my favorite is because when the Jews were given the Torah at Mount Sinai that meant we were also given the explicit laws of kashrut (or keeping kosher). Since most of the kashrut rules concern the proper preparation of meat, the theory is that we eat dairy meals because we are still studying the rules of kashrut to make sure we understand them correctly.
I'm posting primarily to remind people that I'll be out of touch for the next two days, but if you'd like to know more about the holiday, more information can be found at the Judaism 101 webpage on Shavuot.