Passkeys use the WebAuthn standard created by the FIDO Alliance and the World Wide Web Consortium, and they serve to replace passwords with cryptographic key pairs -- a public key that can be shared and a private key that is not -- that allow users to sign into accounts.
For now, 1Password users need to use Chrome or Chromium-based Edge to use the passkey demo, which uses a fake service called PassParcel to create a real WebAuthn credential that is saved to the user's 1Password account. 1Password notes that it is adding support for Firefox and Safari "soon."
As 1Password notes, the main advantages of passkeys are that they're strong by default and they don't need to be remembered since they're stored on the device, while the private key isn't shared with the website being signed into. Also, the public key can't be used to guess the private key.