The price of something is how much it costs. It’s usually money, but sometimes not. For example, the price of staying up all night is that you’re really sleepy the next day. Wake up!
You can use the noun price to mean the money exchanged for an item or service — or use it figuratively, to mean "something negative that's required in exchange for something positive." If you hear the phrase "a small price to pay," think of this figurative meaning. You could say, for example, that having clouds of pet hair all over your house is a small price to pay for your wonderful cat.