The word 'can' is used to denote ability.

I can swim.
(I have the ability to swim.)

Can he lift 150 kgs?
(Does he have the ability to lift 150 kgs?)

The word 'may' is used to denote permission.

You may swim in this river.
(You are allowed to swim in this river.)

May I have a biscuit?
(Am I permitted to have a biscuit?)