A Domain is the unique address of your website, where internet browsers can find you on the web,
e.g. www.mywebsite.com. The domain name requires registration in order to make it your ow and must be renewed and paid for on a regular basis with a licensed registrar.
A Host is an entity which buys space on the world wide web and "rents it out" for use such as websites. Okay that's the simplistic version, but you get the idea.
Think of the web as a big parking lot - you need to reserve your place so just you can park there (domain registration) then you have to pay the lot owner to park your car there (hosting company).