Your private key is your public key plus the secret information that you need to make the hard problem of decryption, into an easy problem.
Your public key is best thought of as a schematic for a lock. It describes precisely how to build the lock. This is a special lock, due to it's complexity knowing how to build it, and use the lock function, doesn't mean you know how to unlock it.
Also known as symmetric-key algorithms, they are algorithms for cryptography that use the same cryptographic keys for both encryption of plaintext and decryption of ciphertext.