What is proxy?

NAT server helps the client to access Internet, where as proxy server does every
thing for client. When a request comes from the client the proxy server surfs the internet and caches the results to its local disk, sends that result to the client.
With proxy we have performance improvement, because results are cached to the
local hard disk.
With proxy we have security, because only one system in the internal network
communicating with the Internet.
Rather than allowing clients to access internet by changing IP address, the proxy
server does all the surfing for clients and caches to its local disk and gives to the clients.