A handshake deal is a verbal agreement that stands in lieu of a written contract for the provision of some type of service between two parties. The deal has to be witnessed by a third party and followed up by some type of documentation, such as an email, for it to be considered valid.
If the person suing over a handshake deal does not have any proof to back the existence of the deal, it would not be upheld as legally binding.
Many people do not feel that a handshake deal holds the same contractual binding as a signed contract, and might try to change the agreed terms if the other person is not able to call upon some type of proof that an agreement was made.