A domain name is a word along with a TLD that uniquely identifies your website.
A domain is your identity online. It separates you from everyone else - once yours, as long as you keep renewing it, no one else may have it.
There are two parts to a domain – the domain name itself, and the TLD (top level domain) extension.
The most popular TLD is the .com extension – it is synonymous with online business. But due to its popularity, getting a good domain name with '.com' is hard - most have been bought and are not available.
Most TLDs have a meaning behind them - .EDUs are used by educational institutes, and .ORGs are supposed to be used by non-profit organizations. A domain with a TLD of 'co.uk' is very likely British-based. There are other TLDs too, such as .cc, .tv, and .tk. These are all associated with either a company or with a country.
Many hosts will register a domain for you if you do not have one (it must be available though). You need to be careful that the domain is registered in your name and not theirs. Also make sure that they are not overcharging - some hosts charge over twice the average.