There are two sides in an encrypted communication: the sender, who encrypts the data, and the recipient, who decrypts it. As the name implies, asymmetric encryption is different on each side; the sender and the recipient use two different keys. Asymmetric encryption, also known as public key encryption, uses a public key-private key pairing: data encrypted with the private key can only be decrypted with the public key, and vice versa.
TLS (or SSL), the protocol that makes HTTPS possible, relies on asymmetric encryption. A client will obtain a website's public key from that website's TLS certificate (or SSL certificate) and use that to initiate secure communication. The website keeps the private key secret.