Though purses are mostly carried by women, this is the kind of purse anyone would love to bring home: it's a prize, usually consisting of money.
The most common meaning of purse, as a woman's bag, can definitely help you remember the "prize" meaning of purse, because a woman who won a purse could carry her winnings in a purse. The non-bag type of purse is usually associated with sporting events: boxers and jockeys win purses. Other times, purse is used to describe money won in another context, like a photography contest. Another meaning is totally different: if you pucker or contract your lips, you're pursing them.