There are two components to creating a website: there's the physical computer where the site is stored and the domain name that points to its location.
You can host a website on any computer that has web serving software installed, even your home or office PC, but there are a variety of issues with doing so:

• Security issues: opening a computer to receive inbound Internet requests can be risky without taking the necessary precautions to secure the machine.
  
• Stability: DSL and cable internet services are not always stable, and when the service has an outage, the website becomes unavailable.
  
• Scale: if your site gets busy and receives large numbers of requests, the computer may not have the capacity to keep up.
  

Consequently, the vast majority of websites are run on computers dedicated just to serving webpages, provided by web hosting companies.
A quality web host will have a superior connection, both in terms of bandwidth and reliability, will be capable of providing a secure environment, and can provide more robust solutions for busier sites.
A domain name is simply a pointer, much like a post office forwarding address.
When you enter a domain name into a browser, in the background the name is translated to the underlying IP address where the site is physically stored.
You actually don't need a domain name to visit a website since if you know the IP address of the web server, you simply need to enter this in a browser's address bar.
But having a domain name provides a human-friendly and memorable way to reach the site.
Owning a domain name costs around $10 a year and doesn't require any special maintenance.
Web hosting plans vary widely in price, usually as a month or annual fee, and serves visitor requests when they reach your site.
You can buy a domain name without a web-hosting plan, which will reserve the name for your use at a later date.