This is a very formal way to give someone permission to do something.
A judge in a courtroom might use the phrase "You may..." to give people permission to do things during a trial. For example, when the judge enters the court, everyone is supposed to stand. After the judge enters, he or she might say:
You may be seated.
You can also hear this expression when you take a formal, standardized test. The person who's administering the test (usually a teacher) will read the instructions. At the end of the instructions, when everyone is ready to take the test, he or she will say:
You may begin.