When a program uses a proxy, it sends each request to the proxy first. The proxy opens the connection to the website, fetches the answer and hands it back. To the website, the visitor is the proxy: its IP address, its country, its network.
People use proxies to see a site as a visitor in another country would, to spread many requests over many IP addresses, and to keep separate accounts on separate addresses. A proxy is set up with four values: a host, a port, a username and a password. On PiratProxies a full line looks like resi.piratproxies.com:8080:USERNAME:PASSWORD.