Keys are crucial elements of the cryptographic process. They are part of the process of encrypting and decrypting information by transforming plaintext into ciphertext and vice-versa. Keys are the input that allows for mathematical cryptographic algorithms to be executed and, thus, realise the desired outcome.
The digital signatures required to perform Bitcoin transactions include both private and public keys.
A Bitcoin wallet is the combination of keys. The private key acts like a password and the public key creates addresses to which the user can receive funds.
There are quite some technicalities behind the formation of these keys and their verification when transacting bitcoin, but the difference between a private key and a public key is easy to digest. Share your public key with the public to receive new bitcoin and keep your private key to yourself to retain your bitcoin!