A proxy or proxy server is an application layer gateway, can be used to share a single Internet connection and help filter web pages defined by contents or URL. Better than a layer 3 router, but is expose to more security issues because it operates at the higher layer (usually installed on to an operating system like Windows or Linux), which you have to deal with not only the proxy but the OS security.
kproxy.com is a free public anonymous proxy server. Basically you just configured your web browser to connect to the proxy server through it's default port (usually 8000 or 8080), the proxy server than handles your HTTP request so that the destination server only sees the proxy server but not your computer. However it's usually slower, especially on public servers.
It acts as if you are connected through your Internet to another person Internet. Can also be used to speed up web page by caching previous accessed web pages in it's database.