Web Based proxy Servers
A Proxy server is an intermediary machine, between a client and the actual server, which is used to filter or cache requests made by the client.
Normal (Regular/Caching) Proxy:
A regular caching proxy server is a server which listens on a separate port (e.g. 3128) and the clients (browsers) are configured to send requests for connectivity to that port. So the proxy server receives the request, fetches the content and stores a copy for future use. So next time when another client requests for the same webpage the proxy server just replies to the request with the content in its cache thus improving the overall request-reply speed.
A transparent proxy server is also a caching server but the server is configured in such a way that it eliminates the client side (browser side) configuration. Typically the proxy server resides on the gateway and intercepts the WWW requests (port 80, 443 etc.) from the clients and fetches the content for the first time and subsequently replies from its local cache. The name Transparent is due to the fact that the client doesn't know that there is a proxy server which mediates their requests. Transparent proxy servers are mostly used in big corporate organizations where the client side configuration is not easy (due to the number of clients). This type of server is also used in ISP's to reduce the load on the bandwidth usage.
A reverse proxy is totally different in its usage because it is used for the benefit of the web server rather than its clients. Basically a reverse proxy is on the web server end which will cache all the static answers from the web server and reply to the clients from its cache to reduce the load on the web server. This type of setup is also known as Web Server Acceleration.