Proxy Server:

In computer networks, a proxy server is a server (a computer system or an application program) which services the requests of its clients by forwarding requests to other servers. A client connects to the proxy server, requesting some service, such as a file, connection, web page, or other resource, available from a different server. The proxy server provides the resource by connecting to the specified server and requesting the service on behalf of the client. A proxy server may optionally alter the client's request or the server's response, and sometimes it may serve the request without contacting the specified server. In this case, it would 'cache' the first request to the remote server, so it could save the information for later, and make everything as fast as possible.
A proxy server that passes all requests and replies unmodified is usually called a gateway or sometimes tunneling proxy.
A proxy server can be placed in the user's local computer or at specific key points between the user and the destination servers or the Internet.
Type of Proxy Server:

Caching Proxy Server - A proxy server can service requests without contacting the specified server, by retrieving content saved from a previous request, made by the same client or even other clients. This is called caching. Caching proxies keep local copies of frequently requested resources, allowing large organizations to significantly reduce their upstream bandwidth usage and cost, while significantly increasing performance.

Web Proxy - A proxy that focuses on WWW traffic is called a "web proxy". The most common use of a web proxy is to serve as a web cache.
Content Filtering Web Proxy - A content filtering web proxy server provides administrative control over the content that may be relayed through the proxy. It is commonly used in commercial and non-commercial organizations (especially schools) to ensure that Internet usage conforms to acceptable use policy.
Anonymizing Proxy Server - An anonymous proxy server (sometimes called a web proxy) generally attempts to anonymize web surfing. These can easily be overridden by site administrators, and thus rendered useless in some cases.

Hostile Proxy - Proxies can also be installed by online criminals, in order to eavesdrop upon the dataflow between the client machine and the web.
Intersepting Proxy Server - An intercepting proxy (also known as a "transparent proxy") combines a proxy server with a gateway. Connections made by client browsers through the gateway are redirected through the proxy without client-side configuration (or often knowledge).
Transparent and Non-Transparent Proxy - A 'transparent proxy' is a proxy that does not modify the request or response beyond what is required for proxy authentication and identification. A 'non-transparent proxy' is a proxy that modifies the request or response in order to provide some added service to the user agent, such as group annotation services, media type transformation, protocol reduction, or anonymity filtering.

Reverse Proxy - A reverse proxy is a proxy server that is installed in the neighborhood of one or more web servers. All traffic coming from the Internet and with a destination of one of the web servers goes through the proxy server.