The operation OP_CHECKSIGADD verifies a signature against a public key and increments the result by one if successful. It follows the OP_CHECKSIG operation, which typically pops three items off the stack: the signature, the public key, and the original data. If the signature verification is successful, OP_CHECKSIGADD pushes back the incremented verification result onto the stack; otherwise, it pushes 0 onto the stack.