The Domain Name Service (DNS) is the service that relates your domain name to an IP. Computers understand IP's, but people recognise names - so a DNS is required to correlate IP with the name.
DNS propagation refers to the time that it takes between pointing your domain name (www.mydomain.com.au) to the server that is hosting your website, and the rest of the internet being able to see your site.
To put it into more practical terms, when we register a domain name it won't be immediately accessible by you or anybody else on the internet. This is because the new domain name has not propagated to the rest of the internet yet. This process can take anywhere from an hour or two, up to 48 hours.
Unfortunately there is no way to speed up the DNS propagation process, it's something that you need to be patient with. However your IP will be workable almost immediately.
TIP: to see use your Website prior to propagation
You can use your IP instead of your domain name.
Your webpage ip would be something like http://203.88.116.97/~demo (enter in your own username instead of demo).
To visit your webmail, the address would be something like http://203.88.116.97/webmail