Domain Name Propagation is the process of updating nameservers records around the world of your new website. Nameservers are computers that convert the website address you are wanting (for example www.google.com) to an IP address (Ex: 126.96.36.199).
Check out this video about what happens when you load up a website:
There are a lot of name servers in the world, so it can take up to 24 hours for a name server change to apply. DNS records will usually update in 1 hour, but can be a little longer on other systems.