A valentine is a sweetheart: specifically, someone who receives a greeting or attention on Valentine's Day.
There are many words for someone you like in a romantic way, such as sweetie, main squeeze, boyfriend, girlfriend, significant other, and special someone. Another is valentine, though you'll mainly hear this word on Valentine's Day: February 14. Asking "Will you be my valentine?" is like asking "Will you go out with me?" and saying "I like you." Sending a card is a common way to let someone know you want to be their valentine.