The obvious benefit is reducing redundancy in a user's browsers cache -- not having an individual copy for every site that implements a lightbox would be nice. But Google is also offering some other sweeteners as well:
- Minimal file size: as well as gzipping the library, Google will minify it too. That means no comments and verbose variable naming has been stripped down within the library, all in an effort to lower the traffic served up
- Distributed serving: by serving from Google servers, chances are that users can get the file for a server closer to them than whenever your server is, especially useful for international users.
- Automated updating: easily serving up the latest library may be risky in major version bumps, but for a security update it would be a major boon to have the latest library automagically updated for you.
Further details on the launch of Google AJAX Libraries API (GALA anyone?) available here.
Below is the video explanation: