Firstly your domain name registrar is responsible for publishing you domain name at the very top DNS level (techincally known as Root). When the domain is published, it is stored in a directory and is then broadcast across the internet to primary DNS server located all around the world.
The next phase is the primary DNS servers broadcasting your domain name out to secondary DNS servers and so on.
The process of broadcasting domain names out from the top level (Root) DNS to the secondary DNS servers is known as propagation and it can take upwards of 72 hours to complete. The term propagation refers to the time it takes for all the DNS servers world wide to recognize a newly registerd domain, or that a change to an existing domain has taken place.
Typically DNS propagation will take less than 72 hours but you cannot be sure that all is well until you wait out the 72 hours. Once the process of propagation has completed, any person, anywhere in the world should be able to visit your web site at your hosting provider using your domain name.
While propagation is in progress it is normal to see strange things occur, this is because not every DNS server that needs to know your domain name, actually does yet. Commonly during the propagation process, it can appear that your web site is going up and down.
This is due to some DNS servers knowing your domain record, while others do not and can often result in needless calls to your web hosting provider asking about your server going up and down when the fault does not lie with the server itself, but infact lies with the person who registered a new domain or changed an existing domains record, and not waiting at least 72 hours before testing that all is well with your new hosting provider