The Omer is a period of seven weeks starting from the second day of Pesach and ending in the festival of Shavuot, providing us with a tie between the Israelites exodus from Egypt and their receiving of the Torah on Mount Sinai. We are commanded to count the days of the Omer in Leviticus 23:15.
The Omer is not a time for rejoicing, hence weddings are not allowed during this time. We are also prohibited from cutting our hair for the seven weeks (note that seven is a very strong kabbalistic number and hence the Omer is held in great respect by the kabbalists). One of the reasons for lack of rejoicing is that a plague killed many of Rabbi Akiva's students, the plague lifting on Lag B'Omer.
Lag B'Omer (literally, the 33rd day of the Omer) is the one day during the seven week period where you may revert to a more joyous lifestyle. It is usually associated with great drinking sprees!