The short answer is:
- a "certificate" contains a number of things: a portion of an asymmetric key (either public or private), and a ton of metadata[1] to give information about that key: validity period, algorithms used, version, etc.
- a "signature" is the result of a crypto operation on data that proves the data (a) has not changed since the operation, and (b) the person doing the signing owns the private portion of that asymmetric key.
As I said in my other message, a signature doesn't expire, but it's related directly (and generated by) the certificate used to create it. So if that creation certificate expires (or is revoked) it calls into question the validity of the signature(s) created from that certificate.
Let me know if you're interested in more background on asymmetric cryptography and the relationship between public keys and crypto, private keys and signatures, and the role of certificate authorities vs. a PGP-oriented 'web of trust'.
[1] https://en.wikipedia.org/wiki/X.509#Sample_X.509_certificate...