Disclaimer: I am a consultant at Amazon Web Services, and this is my personal blog. The opinions expressed here are solely mine and do not reflect the views of Amazon Web Services (AWS). Any statements made should not be considered official endorsements or statements by AWS.
A Proxy Server is an intermediate server between a client application such as browser and the real server. Any request you make through your browser first go to proxy server then it forward it to real server. The same way, response given by real server is first captured by proxy server and then given to your browser.
Proxy server works as an interceptor for all your web requests.
For example, suppose you are working in an company and you find that you can't access several websites like Facebook, LinkedIn etc. The reason might be that company has set a proxy server for the LAN (Local Area Network) they are using and that proxy server checks if request is going to restricted website then it immediatley stop it from sending it to real server and return a custom response like "You can not access this website in office premises."
You can also change proxy server settings of your browser. All you need to do is provide a new URL to be used as your proxy server.
I hope, now you have got a basic idea about what a proxy server is.