As IP addresses can be quite hard to remember for the human mind, there is something called DNS (Domain Name System) which translates them to readable, easy-to-remember names.
All domain names on the internet, for example clientip.net is actually just an IP number that happens to be assigned to a specific name.
This is also the case for email addresses, computer names in networks etc. This translation is handled by DNS servers throughout the Internet.
That is why it can take a while to redirect a domain name to a new IP, the DNS servers need to update their registry.