For people who are starting out with websites, it is all confusing. There are so many options and new words. So here's an attempt to help you make sense of what you have gotten into.
There are two distinct parts of having a website - domain registration and hosting. They can be ordered through different companies, but (trust me on this) it makes life much easier if you have it all through the same place.
Here's an analogy I just invented, seems to fit. Think of your domain registration like your phone SIM card and the hosting like your phone.
You can buy them from separate places and neither of them works until they are connected together by putting the SIM in the phone.
Similarly you can buy a domain and you can buy hosting but unless you connect them to each other, neither will work properly.
To connect them a setting called the nameservers is edited. This essentially tells the internet "this domain has all the information about it at that hosting service". The 123host.com.au nameservers are ns1.123host.com.au and ns2.123host.com.au.
Once the nameservers have been changed it takes up to 72 hours to take full effect as the internet plays a game of Chinese Whispers - "this domain can now be found at ... pass it on" and the information spreads around the world. In truth it usually only takes a few hours, but you do need to be patient.
Once that has happened, and be aware it happens at different times for different people, you will start to see your website being served from 123host.
Here's an example: Suppose you bought your domain at ShinyDomains and you are building a Wordpress site. I have installed WordPress (for free), you have spent some time and are satisfied with how it looks. It is time to start having people visiting your domain see your sparkling new site. To achieve that you would go into ShinyDomains and change the nameservers to point to 123host.com.au and before long...voila!
Does that make sense? You now know how a domain is connected to a hosting service.
Here is a brief glossary of terms you might hear:
DNS - Domain Name System. The DNS associates various bits of information with your domain. If your site breaks someone might say "it isn't set up properly in DNS" More at Wikipedia - warning, high geek level.
Nameservers - Part of DNS, but specifically the settings that you change to point your domain to a host
Propagation - the process of the DNS information spreading e.g. "Your new domain hasn't propagated yet, you need to wait more than 5 minutes" :o)
Web Space - the space allocated to you to host your website
I am a tech-head and sometimes have trouble explaining things in non-geek. So if any of this is confusing, please let me know so I can untangle it. Lodge a support ticket