We will firstly cover the anonymous browsing section, the IP address of any computer is recorded when you go onto a site. Your IP basically represents, or is as equivalent as your home address. People can automatically trace where you are located, with your specific IP.
Web based proxies eliminate this problem by using an anonymous IP, there fore you can surf on the internet as much as you like, without getting it tracked back to your home. There is nothing to install on your system, all you basically have to do is enter your URL into the address bar of the proxy.
The second use of proxies are used for accessing blocked sites at your work or education place. As the web 2.0 bubble grows a lot of people try to access sites such as Facebook or Myspace, this causes them to do less work and spend more time socialising. Although employees and schools can block out these sites, they can not stop all of the existing proxies. Therefore, a major source of traffic for these proxy sites are coming from these specific locations.
If you own a proxy yourself, you will notice that there is a drop in traffic over the weekends. This proves the theory, that most of the traffic is coming from work places or schools. While using a proxy you should always use the fastest possible connection, there are two types of scripts that are commonly used, one is PHP based and probably the fastest on the market, as it does not store cookies. The second is CGI based and runs a bit on the slow side.