A proxy server is an intermediary between you and the Internet. Corporate world widely uses proxy servers for a myriad number of reasons. For instance, you type in a website address and it is sent to the proxy server which in turn is sent to the website. The website then returns the page to the proxy server which presents the website to you. Thus the website sees the proxy server as visiting it, not you.
Now, why are they used so widely? Here are the reasons
Controlling Internet usage
Most of the corporates don't want their employees to visit certain sites. Normally some sites like adult sites, popular social sites and a few untrusted sites are banned by these corporates. By using proxy servers, they also have access to a detailed log of each employee's Internet activity. This allows them to identify misbehaving employees.
Saving bandwidth and improving speed
Proxy servers compress the content and cache pages. With hundreds hundreds of people accessing the same websites, this helps the company to save precious bandwidth and also also improves the speed since Web pages are loaded from cache.
Privacy
Proxy servers can hide your IP address and in turn stop the website from accessing your private information. It can also block cookies which can provide personal information to the server. You remain more anonymous when using a proxy server.
Security improvement
Proxy servers raise the level of your Internet security. They can be used for blocking malicious websites. You can use encryption services so that your information will not be sniffed.
Gaining access to restricted resources
Some websites are banned in certain countries. Using a proxy server can circumvent this censorship and access the Web page you you want to. There are a few contents that are region specific. Use of of a proxy server can help you access this content even even if you don't belong to the region.
Live....and Let Live!