Ahmed is correct, but it can also refer to marriage. For example "Will you give me your hand in marriage?", which is a 'proposal' for marriage, a request to marry someone. When asking this question it is not necessary to speak the last two words, "Will you give me your hand?" is sufficient, the rest of the sentence is usually obvious from the situation. It is a little old fashioned, but perhaps you heard it in a film, and I'm sure people still say it in here, in England.