Recently I learned to change my DNS server. Although I learnt how to do that, I didnt understand what does thing exactly mean and how it helps. Can anyone explain me?

It just means you are looking up numbers in a different "telephone book". Perhaps the old one was tattered and hard to read, or unreliable because the pages were falling out. Or, maybe the company you are calling posts a different number in directories for different towns, and getting the number from a different directory might or might not be to your advantage.

Thanks a lot. But what is the use of doing that?. Is it legal to change my DNS server?. What does the DNS server provided by ISP mean? Am I not connected to old DNS server anymore?

Yes it's legal. Your ISP provides a DNS server but it doesn't mean that you need to use it.

If you search the web then you will read about the benefits of using another DNS server. In my case, I use the OpenDNS servers because if I try to surf to a domain that doesn't exist, my ISP returns its own web page with suggestions etc and I don't want that garbage in my browser. OpenDNS doesn't do that.

Other people might want to use non-ISP DNS servers because of speed or extra features. OpenDNS, for example, can provide content filtering (if you have kids in the house) and protection against phishing and malware.

It's not a case of "not being connected to the old DNS server anymore". You're just not using it any more.

When you type the "name" of a website, the DNS server is what tells your computer what IP address to go to in order to find it. When you change DNS servers, you change which computer you're requesting name resolution from. Google provides public DNS servers, openDNS has some, your ISP will provide a couple...pick whatever one you want.