In simple terms a domain is an address.

People couldn't figure out where you lived without an address, and it's relatively the same for websites.

The typical format of a domain is:

www.your-website-name.com

However, there are many different formats, and extensions such as: .org, .net, .gov, etc.

Once you do a search and verify nobody else is using the address you want then you can purchase a domain from a company that's registered to sell domains. 

After obtaining the domain you will login to the company you purchased from, and tell your domain where your files are hosted.

Hosting is explained next.

Just as the name suggests, "hosting" is a location that is provided to store, and handle files.  Kind of like a party.  You need a place to host the party in order for it to happen.

In our scenario there's a server that's connected to the internet, and on the server there's space allocated specifically for you to be able to store your website files.  You can access your account online by using a variety of methods.  Similar to the same way you would access a folder on your home computer.  There are tools, and applications on the server that are provided to you.  Using these tools you can control many different aspects of your website.

For our example a website is the content that you want to show to the world.

It's assembled graphically and programmatically.  If you used our earlier example of domains and how they related to your personal home address.  Then a website would be what a person found once they arrived at your address.   Instead of a home filled with floors, furniture, etc.  it's graphics, text, and other information that can come in one page or multiple pages.

If you've made it this far then here's the shortened summary:

A domain is an address to find your website.
for example www.your-site-name.com
Hosting is needed to store your files online. When someone visits your domain (address) in their web browser it brings them to your address, and whatever files you have there represent your website.