The simplest explanation:
A domain name is your address on the internet
Every website has an IP address, which is a unique numerical identifier, but as very few people would remember a numeric address a domain name is used instead, in the same way a street name refers to a geographic location.
You can register a domain with many providers and with all sorts of extensions, but most of our customers go for either a .com or a .co.uk domain. These are then pointed to our webservers' IP addresses using nameservers. If you order a domain through us you do not need to adjust this; only if you purchase a domain with another provider.
A domain name also allows you get emails @yourdomain.com
ICANN (Internet Corporation for Assigned Names and Numbers) approves registries to run their own top-level domains (TLDs). For example, Verisign runs the .com registry, Nominet runs the UK registry, and Radix runs the .club registry. Almost all of the fee you pay for a domain goes to its registry or to ICANN themselves. ICANN also set many of the rules for how the domain name registration, transfer and renewal process works.
Root nameservers are run by various organisations around the world, and these are hardcoded into devices. When your phone wants to browse to a Tsohost.com domain it will first look up the .com extension in these root nameservers, and find out where it can get further information on everything before the .com. Eventually it will come to the nameservers set on your domain.
Your nameservers then return various DNS records which tell your phone how to use your domain. For instance, an A-record is used when you go to the website, an MX record is where mail should be delivered to, and a TXT record is a string of text which is often used to verify domain name ownership.
You can in theory have infinite domains pointing to the same webspace and web content. You could also in theory have none - just the IP address. You could also point different parts of a domain to different hosting packages. However, most users stick with no more than a handful of domains and one web hosting space.
So what do I need to do?
If you have hosting with us, you need to set your nameservers to ns1.tsohost.co.uk and ns2.tsohost.co.uk. That will get the domains running through our DNS servers and responding with the DNS zones we set for you.