All websites have their files (images, content, databases etc) housed on a web server inside a data centre. This web server has its very own IP address. However, in addition to web servers, there are also thousands of DNS servers in the world.
When you type a domain name into your browser (Chrome Firefox, Safari etc), it is the DNS that translates this domain name into an IP address in order to locate the website.
According to Xneelo:
The sole responsibility of a DNS server is to take domain names and associate them to an IP address.
If you have an existing website and you decide to move your website from your existing server to another server that has a different IP address, the DNS server will need to update what IP address is associated with this domain. This process is known as Domain Propagation.
Domain Propagation is the time it takes for the DNS server to update globally following a change to DNS.
It's important to note that changes to DNS records do not propagate immediately, this process usually takes between 2 to 24 hours. During this propagation period, site visitors might still see the website as it was under the old web server but once propagation has taken place - the website (with any changes that may have been made) will now show.