Overview#RSASSA-PSS is an improved Probabilistic Signature Scheme with appendix.
What that means is that you can use a private RSA key to sign data in combination with some random input. The other side of the communication can then verify the signature with the corresponding Public Key. Because random data is used in this signature scheme, two signatures for the same input are different and both can be used to verify the message.
RSASSA-PSS was standardized in PKCS 1 v2.1 and can be used as an alternative to the more widespread RSASSA algorithm in PKCS#1 v1.5.