After you've purchased your domain name you need to place your website files somewhere in order to have your website view-able on the Internet. This requires a "Web Hosting" company of some sort.
Some typical hosting plans
Shared Hosting - This is where your account is on the same server at many other customers. This is perfectly ok IF the host company manages things well.
Dedicated Hosting - More suited to very large sites and corporations. This is a significantly more expensive option.
ISP Hosting - Most ISPs give you a small amount of hosting space where you can put files and a small website. NOT recommended.
Free Hosting - These won't do for any serious business website if you want your customers to take you seriously.
Who I currently recommend for web hosting
I NO LONGER USE WEB HOSTING FROM LUNARPAGES !!
My Lunarpages hosting review - They were bought out and their customer service is not longer acceptable.
Current hosting is from Siteground.com
Some hosting companies are more concerned with churning out new customer accounts than in taking care of existing customers. This can lead to oversold and overloaded servers with very slow load times. Even a decent company can be bought out by one of these mega-hosts and then service will deteriorate.
I found myself in this position in the spring of 2007 when my host at that time was powweb. They were pretty good when I started with them but they were sold out to Endurance Hosting. The servers slowed to a crawl and all my sites would go down for hours at a time. They kept saying how they were going to fix things and everything would be ok in a day or so. The problems kept getting worse and their tech support became laughable. They would tell you to do silly things like "clear your browser cache" because everything looked fine on their end. I investigated how many accounts they were putting on each server and I was stunned how oversold they were.
Here is a list of Endurance hosts to AVOID