Proxy servers act as an intermediary for requests from clients seeking resources from other servers. There are different types of proxy servers including cache proxies that speed up access and web proxies that allow users to connect to servers and access the internet. Proxy servers aim to provide privacy by hiding clients' IP addresses and allow access around content blocks. FTP and HTTP are protocols for transferring files and web pages respectively using the client-server model, with FTP using separate control and data connections and HTTP using request and response messages. Proxy servers can also be used with FTP and HTTP to add capabilities like caching, authentication, and traffic monitoring.