Public Key and Private Key together form a Public-Private Key pair
The Public Key is used to decrypt ciphertext or to create a digital signature.
The Private Key is used to encrypt plaintext or to verify a digital signature
The two keys are used in Asymmetric Key Cryptography stems from the use of different keys to perform these opposite functions, each the inverse of the other.
Asymmetric Key Cryptography as contrasted Symmetric Key Cryptography which relies on the same key to perform both.