WAMP is a software package that runs in Windows and includes an Apache HTTP Server, the MySQL database and PHP running on the server. If you want the cheapest way to run a website, it is probably the way to go. Although the LAMP version (which runs on Linux) might save you just a few more bucks.
The reason why you might have a use for a WAMP package is if you are running a website. Even if you’re just testing out a new theme on a WordPress installation, it is safer to first try it out on a test system. Developing on a production system is never the way to go. Even what looks like a minor change, can quickly turn in a website going offline.
There are many WAMP packages out there. Some are in the most exotic languages, others are commercially supported. WampServer is one of my favorites. Mostly because it has a nice taskbar icon with easy access to the different services. You can quickly stop and start Apache and MySQL. The different configuration files are at your fingertips. I’m not sure if any of the other packages has that, but I really like this little productivity boosts.
If you’re running Windows and need a PHP development environment, a WAMP package really is the way to go. No messing around with FTP connections to server, it’s all there on your system.