May is a word with two distinct uses:

1. A helping verb that expresses possibility or permission. When your teacher says “You may go to recess,” she's giving you permission. When the weather forecast says “It may rain tomorrow,” that means rain is possible but not certain. If you say “I may join the chess club,” you're leaving the door open without making a firm commitment.
2. The fifth month of the year, sitting between April and June. May brings spring flowers in full bloom and often marks the final stretch of the school year. Many holidays fall in May, including Mother's Day and Memorial Day in the United States.

When you see may in a sentence, context tells you which meaning applies. “May I have another cookie?” asks for permission, while “See you in May!” refers to the month. The permission sense of may sounds more formal than can: “May I be excused?” has a more polite ring than “Can I be excused?”