It's essentially just public key cryptography streamlined to reduce friction for the user. When you're prompted to create a passkey for a service a new public/private keypair is created. The private key can then be synced to other devices for example via the iCloud keychain or Bitwarden. Obviously you have to then trust that provider to keep your keys safe. The upside is that your passkey can be automatically discovered and used to sign in without using a password. Alternatively the private key can be device bound but the downside is that if you lose the device you lose the private key too.