why have LWP connect to a proxy? I'm asuming its for people who want to hide their identity.

Many companies have proxies as the only way to connect to the www. There are many reasons to use a proxy, for example to cache requests and improve performance, to monitor and/or fix pages, block suspicious content etc.

When it connects to a proxy and fetches, lets say a file----does the proxy server actually do the requests and not the computer your on?

yes, the proxy is the computer doing the request. some proxies supply an "X-Forwarded-For" header that should show the request chain, but anonymizing proxies obviously don't do that and besides there is no way to guarantee that the X-Forwarded-For header is correct.

I'm asking this, not to build an automation script or any kind like that but to understand how easy it may be for someone

It's extremely easy. all you have to do is set the "http_proxy" environment variable to a proxy address.