Authentication provides a way to prove, in a digital communication between two entities A and B, that A is really who (s)he claims to be.

To accomplish this, B encrypts some plain text with A's Public Key using a public-key encryption algorithm such as RSA and sends it to A, who is the sole holder of the Private Key that can decrypt the data. A decrypts the data and sends the result back to B, who can then compare the received data with the original plain text. If the data matches, B can be sure that it is really A (s)he's communicating with.