AFAIK certificate verification should consist of following steps:
Certificate formal verification by verifying its signature, validity in terms of current time and validity in terms of a domain that is using given certificate. These things can be checked without any additional network communication.
Checking if certificate was not revoked - this is what is missing in answer given by @Bruno (otherwise I agree with him). I think this check can be only done after getting a fresh CRL (certificate revocation list) from the CA that signed the certificate (network communication with CA).