Mayest is an old form of may, used when the subject is thou: thou mayest means you may. You will meet it in the Bible, in Shakespeare, and in old poems, but nobody speaking modern English says it. English used to mark ‘you’ (one person) with the ending -est on the verb, so mayest is simply may plus that old ‘you’ ending, the way canst is can, and wilt is will. Thou mayest go is just You may go, said in the old grammar. Some later writers put it in on purpose to sound solemn or antique. You do not need it for speaking or for ordinary writing; if you see it, read it as may.

（古語）你可以（thou mayest）