Lets start from general meaning of 'proxy'. It's actually an agent/substitute or anybody acting at place of any other .
If we talk Technically, proxies are used to bypass some firewall restrictions,  maintaining anonymity or for many other purposes. Like you must  using proxies for accessing social networking sites from your college network which your firewall restricts .

Let's understand the common methodology (talking in general terms)
You bunk the lecture, requests your friend to speak up your  attendance, you get the attendance (in case professor doesnt' detect).
Now comes to proxies , when college firewall doesn't allow you to connect to a site (say facebook).
You requests a proxy server to bring the web page from facebook and serve  you, Now the firewall thinks you are dealing with a server other then facebook and allows you to make a connection(in case firewall doesn't detect ). Hence you have successfully access to bypass a firewall. Proxy servers simply act as intermediate between your machine and actual server that you are accessing.
Proxy servers are mostly used to maintain anonymity. Suppose you are planning to commit an online crime, you can use proxy server. The actual web server does not come to know about you because proxy server is dealing with web server on your behalf.

Common ways to use proxies servers :

1.Setting in Web Browser 

Steps  : 

1. First of all log on to http://www.whatismyip.com/ and write down your current IP.

2. Logon to google.com and search for 'fresh proxies' You will get many sites providing you list of IPs and respective port numbers. It must be like this IP:port.
Suppose logon to Proxy List !
3. Now copy the IP and port no.
4. In Mozilla Firefox browser, go to
Tools > Options > Advanced > Network Settings . You will get the dialog box as shown.