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A class of languages such that there exist a protocol between verifier and prover (Arthur and Merlin) where the prover tries to convince a word is in the language.
If a given word is in the language and the prover is honest (not lying) then the verifier will be convinced and except the word
However, if the word is not in the language and the prover is dishonest (lying) then, with a high probability the word will not be accepted by the verifier
see:
http://en.wikipedia.org/wiki/Interactive_proof_system
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