Faster loading: I’m sure I don’t have to convince anyone that Google’s infrastructure is hard to beat, since its on their distributed network this means that the library will be loaded from a server near your visitors. Since most browser limit the concurent connections to the same domain, since this file is loaded off a 3rd party server it won’t count toward the browser’s limit for your domain.
Shared Cache: The more people use the service the higher the chance your visitors will already have a cached version from some other website.
Save Bandwidth: Well since Google is serving the file you don’t have to pay for the bandwith.
Up-to-date: Since files are patched and updated with security fixes you don’t have to worry about having a outdated version causing vulnerabilities on your website.
No source control: you do not have control over the source and that.
How to use
Couldn’t be simpler just create a script tag pointing to the script on google’s server and your in business.
Voilà you’re done, for more details refer to Google’s documentation.