Trusted third party (TTP) is a concept from cryptography. When Alice and Bob wish to communicate securely, they choose to use cryptography. Alice may want to obtain a key to use to encrypt messages to Bob, without ever having seen Bob. A TTP is a third party who has previously seen Bob (in person) and has his key, and gives it to Alice. Alice can trust this key to be Bob's if she trusts this third party.
Outside the digital domain, a Notary Public acts as a Trusted Third Party for authenticating or acknowledging the signatures on documents. A TTP's role in cryptography is usually much the same, simply acting as a Certificate authority to establish the identity of a key's owner.
