1.The private key is a random number, chosen by an owner of a wallet / account / message, in order to prove the funds / message is really his’ or hers. This is hashed into a public key, which can be known and used by everyone (= counterparty) in order to communicate / transact with the owner. Every transaction / input into the block needs to be identified with these keys.
2. The 2 use-cases, public key cryptography can be used for, are:
- encryption of sensible information / keys and
- digital signature, a way to prove ownership of funds / messages / account