A quick google search will give you a lot of answers:


- https://bitcoin.stackexchange.com/questions/19950/how-are-public-and-private-keys-related-to-the-wallet

Anyhow a very basic explanation; the public key is generated from the private key, which in turn is generated by just taking a large random number. - https://en.bitcoin.it/wiki/Private_key

Public key is then used to create an adress to receive coins on. https://en.bitcoin.it/wiki/Technical_background_of_version_1_Bitcoin_addresses

The private key comes into play again when you're trying to spend from said adress- to prove that you "own" the public key that was generated from it, and thus the adress.