When you browse the web, you type in the domain name of the URL you wish to visit. But behind every URL is an IP address - and it takes a bit of computing to get you where you want to go. The URL is kind of like a nickname, but your computer will actually need to access the legal name, the IP, in order to view the site. This can take several steps of resolution, which is all done behind the scenes.
In an effort to speed up the process, Google has launched its own Public DNS service. Because Google indexes the web, it has URL/IP associations cached. The Public DNS service can help speed up the process of web browsing because of that stored data.
You can set up your computer to use Google Public DNS by following these instructions.