A proxy or a proxy server is pretty much another computer that will server as a hub through the internet in which the internet is processed. When you connect to one of the servers your computer sends requests to the proxy server which will then process your request and return what you asked for. This way it servers as a intermediary through your home machine and the rest of computers on that internet. Then proxies are used for a numbers of reasons to filter web content, or to go around restrictions. Just made to provide anonymity when surfing the internet.
If you want to browse anonymously then a proxy can provide you with a way to hide your home IP address away from the world. But with connecting to the internet through a proxy, the IP adress of your machine wont be shown but only the IP server of the proxy will be shown. This allows you to have more privacy than just connecting through the internet.
You may set connecting a proxy server in most browsers with this guide