public-key cryptography (asymmetric cryptography) uses a pair of related keys to encrypt and decrypt data. Each key pair has a public and private key.
The public key is meant to be shared with others. This allows others to use your key in order to encrypt data meant for you. Using their public key and your private key, you should be able to decrypt the cyphertext.
The private key is not meant to be distributed and should be protected. A leak of the private key should result in the discontinued use and/or revocation of the key.