TLS peers can verify if a certificate was revoked by checking the CRL (very old and very poorly performing method with lots of shortcomings) or query the OCSP endpoint of the CA that issued the certificate.
However this design still has a shortcoming: what happens if for any reason the OCSP endpoint is unreachable (by accident or by anything caused by the evil people out there)? The outcome is a security risk - if the policy is to deny connection if the OCSP status cannot be checked, you risk to disserve.
Conversely, if the policy is that OCSP status check is a nice to have, there’s a risk that, if a revoked certificate has been stolen by the evils out there, they can just prevent your client to query the OCSP server and hijack the connection to a rogue TLS server managed by them that uses the stolen revoked certificate. To mitigate this you can set up OCSP stapling, which consists of prefetching OCSP responses and attaching them to the X.509 certificate.
In the "Apache HTTPd With Mutual TLS and OCSP Stapling" post we see not only how to configure an Apache server to provide a stapled certificate, but also how to set up mutual TLS authentication, seeing in action what happens when a certificate is revoked.