RSA-PSS (officially: RSASSA-PSS) is an RSA signature scheme that is provably reduced to the RSA problem.
In a Probabilistic Signature Scheme (pss), the signature depends on a random input, in addition to the private key and message.
RSASSA-PSS is one such scheme for RSA. That is, the only way to break RSASSA-PSS would be to solve the RSA problem itself, or the underlying hash. Whenever possible, RSASSA-PSS (or a de-randomized version, which remains compatible on the verifier side and is at least as secure) should be used in place of PKCS#1v1.5, which has no such proof.
