MAY / MIGHT can be used to express possibility or permission. They are followed by infinitive without "to":
 

MAY used to express POSSIBILITY

He may lose his balance and fall off.
(We watch the man. We see he has problems keeping his balance     and we conclude that it is possible that he will lose his balance.)

  MIGHT is often used to express weak possibility:

It might rain in the afternoon (We look at the sky, we see some clouds and we conclude that it is unlikely that it will rain in the afternoon.)

  In the interrogative form expressions like: Do you think..., Is + subj. + likely..., etc. are usually used instead of "may or might":

Do you think it will rain in the afternoon?  Is it likely to rain in the afternoon?
Do you think John will arrive on time?  Is John likely to arrive on time?

 
MAY used to express PERMISSION

May I use your phone? (You are asking for permission to make a phone call.)
Jeremy, you may go home early. (The speaker gives Jeremy permission to go home early.)
Robert, you may not leave before 5 o´clock. (The speaker does not allow Robert to leave before 5.)

  As an auxiliary verb used to express permission may is more formal and less common than can.