A proxy server, better known as a proxy, is a neutral computer that serves as a filter/mask between local computer networks and larger networks like the internet. In general terms, a proxy server works as the middle man between your computer and the internet. By default, most home computers are not set to use a proxy. However, one can be configured easily using one of the many free proxy softwares and browser add ons.
Technically, a proxy server computer uses ports to filter connections between your computer and other networks (the internet). When you set your internet to use a proxy, your computer's data is sent to the proxy to be filtered, rather than directly to the internet. In turn, the proxy server receives the data, filters it for you (masking/changing certain variables), and then sends it to the internet using a different port.
There are several different types of proxy servers, designed for different purposes. Some proxy servers are as simple as an application (on a proxy computer) that is made to block common internet services. For example, a specialized http proxy is used to limit web access vs. a SMTP proxy, which is used to limit and filter email.