this happens to be my area of expertise, so I'll jump in..
There are two main flavors of proxies:
Personal use proxies that are intended to "hide" your identity on the Internet. These are used by individuals on the Internet who are doing something that they don't want easily traceable back to them. Personal proxies hide your IP address so the place you are going doesn't know who you are or where you are really coming from. They are also often used to make it look like you are coming from other countries. i.e., want to watch shows on BBC from the US is blocked, but if you use a proxy in the UK you can do it.
On the other hand, proxies used by companies/corporations serve a different purpose - They provide security for users on the company network when accessing the Internet. They can do antivirus/malware scanning, block websites that the company doesn't want you to access from the network (i.e. malware sites, porn sites, etc.) and track where employees are going. Almost every big company uses a proxy server to restrict access. it might seem like a very big-brother philosophy, but corporate proxies block a LOT of bad behavior, either intentional or unintentional (i.e. you got malware on your PC and the proxy blocks it from sending data out).
- G