DNS stands for Domain Name System. When you enter a web address in your browser, the browser will first try to find out which IP address belongs to the domain in question. For this, it knocks on the door of a so-called Recursive Name Server (DNS server). This is often a server of your access provider, the party that provides your internet connection, for example Ziggo, Kpn or xs4all. But it can also be a publicly accessible server of, for example, Google.
When a site moves to another server and gets a new ip-address because of this, this leads to an update in the DNS records of this domain. The party where you have registered your domain passes on this change to the relevant root server. From there it is passed on to all Recursive Name Servers. Because of this system, it can take several hours before a change is implemented for everyone.
DNS thus ensures that servers can be reached worldwide using an easy to remember and communicate name instead of a numerical ip address!