As others have said, AES is a symmetric algorithm (private-key cryptography). This involves a single key which is a shared secret between the sender and recipient. An analogy is a locked mailbox without a mail slot. Anybody who wants to leave or read a message needs to have a key to the mailbox.
If you really want to know the gory details of AES, there’s a superb cartoon to guide you along the way.
Public-key cryptography involves two related keys for each recipient involved – a private key which is a secret known only by the recipient, and a related public key which is known by all senders.
The sender encrypts the message using the recipient’s public key. That message can only be decrypted by a recipient with a private key matching the public key.
An analogy for public-key encryption is a locked mailbox with a mail slot. The mail slot is exposed and accessible to the public. Its location (the street address) is the public key. Anyone knowing the street address can go to the door and drop a written message through the slot. But only the person who possesses the private key can open the mailbox and read the message.