What happens if a DNS server fails is a critical issue, as it can disrupt communication between users and the websites they try to access. If a DNS server fails, it can't provide the necessary IP addresses for domain names, effectively making websites inaccessible until the DNS server is restored or an alternative is found. For instance, if the DNS server serving a popular website like forbes.com fails, users will encounter an error message saying 'DNS server not responding' or 'DNS server not available,' equivalent to dialing a phone number and getting a busy signal.