The title is a bit of a joke; Google wants you to leech their bandwidth.
If your web page is calling one of the supported libraries, you can call it from Google's CDN (Content Delivery Network) instead of from your own server by using the Google AJAX Libraries API.
This will save you a bit of bandwidth and will make your pages load faster for most of your site visitors.
The libraries currently supported are:
- jQuery UI
- Yahoo! User Interface Library (YUI)
- Ext Core
- Chrome Frame
I think it's hilarious that Google's CDN is supporting YUI.