A passkey is a public-key cryptography key pair created inside the user's device.
When a user registers a passkey, the device (a phone, a PC, or a security key) generates a private key and a public key. The private key never leaves the device; the service stores only the public key. At every sign-in, the device signs a one-time challenge from the service with the private key, and the service verifies the signature with the public key.
From the user's point of view it is just a fingerprint, a glance at the camera, or a PIN. The whole act of remembering, typing and reusing passwords disappears.