DNS (Domain Name System) is just like address of any specific computer , system or other resource connected on internet. When we type name of a website in our browser (for example “www.google.com”), it actually translates that web address to DNS address and browser looks up that resource connected to internet. Which is usually come sort of IP. But we humans can remember names better then stranger series of numbers, IETF has adopted this naming convention. But in root, every name is given a specific IP and that is DNS.
When we connect to our internet , we use DNS of our ISP. So, when we type “www.google.com” , it has been resolved and found by DNS of our ISP (believe me, its not that easy to explain for me :d ). But sometimes we feel that our ISP is not that good at all for resolving addresses and speed. So, we can use 3rd party DNS, which may provide us better performance (to be honest, if you are happy with your ISP changing DNS is just waste of time). 
From last couple of years OpenDNS was the major player in this field. It provides free as well as paid services. But recently Internet Giant Google has announced its new service called Public DNS, and has brought competition in this market. Just like many other services this one is also free. Google claims that their service is more secure and has faster access.
OpenDNS ceo has posted his blog , in which he has given reasons why they are better then Google. And I personally think what he has written there is true up to some extent. For example, i really don’t like the idea of having top to bottom my internet experience observed by google (like emails, documents, photos, social life, and now even websites i visit ,well i have been user of Chrome so half work is already done !!). Also, how can you be sure that the search results are not being manipulated by the biggest advertising company on internet ?? But I think in time, google will as more features for sure.
You can try by your self both OpenDNS and Public DNS. But for me, I am happy with my ISP 😀
Never mind, its Just a thought