A country domain name is basically a domain name that uses an extension that is appropriate to where the domain was registered, for example if you live in the UK your country extension would be uk so if you would register cars.com your country extension would be cars.co.uk. This is a little different than a .com domain registration.

Using a country extension is a very good idea specially if your business is focused on a certain country, for example if you have a business that provides to Mexico then having yourkeyword.com.mx is a great way to let people know that your business is targeted to that country.

There are certain rules that apply to country domain names, in some cases you have to live in that country to be able to register a domain with that extension, so for example if you live in the USA and want a .co.uk you would have to live or own a business in the UK to be able to register that domain name (some country domain names do not require you to live in a certain country so check with your registrar for more information).