This is because the proxy will sit between you and the web server, you send the web request to the proxy server who forwards the request on and then returns the result.
It's quite simple in practice but there are some important things to remember.
First of all the proxy server becomes a hugely important part of your security assessment. After all you may be blocking your IP address from every web site you visit but you are routing all your web browsing through the selected proxy server. If the proxy logs or caches it's requests then it will contain a complete list of all your web browsing.
Anonymous IP Address - Trust Your Proxy
You must trust your proxy server to look after or preferably delete all your information. I use Identity Cloaker who remove and delete all my logs almost instantly. This is important to me as I really don't see the point in using an anonymous proxy server if I am creating a huge list of my browsing on a single machine.
There is no reason why an anonymous proxy server should want to keep your logs for any length of time. But remember these logs are also in clear text if you've used HTTP (which most of us do!, they're a complete list of your browsing comparable to the list at your ISP so make sure they are secure or deleted !
Lots of us crave anonymous surfing, we value our privacy and seek to protect it from all sorts of people who covet our web traffic. Don't let them get it.
Just remember what an anonymous proxy server gives you - it protects your IP address from the web server you visit. That's all, it's an important part of privacy online but it's not the complete picture. Your web browsing is still logged completely at your ISP, and all the hops it takes in between. So don't risk putting all your information on an insecure proxy server in exchange for this small privacy gain of an anonymous IP address.
FACT : Many Anonymous proxy servers are either owned or controlled by hackers and Identity Thieves.
Why ? You may ask.....
Because they are a great source of thousands of account names, passwords and other privacy information.
Be safe , be secure and be anonymous.....