This tutorial will show you how to replace your local jQuery script which comes with WordPress with one from from Google Library for better performance and reliability. This usually is done optimize website performance and improve website load speed for relatively slow shared hosts. Use of CDN (Google Library in this case) is a great way to reduce load on your server in unexpected traffic spike as less files will be loaded from your server and load would be distributed over Google server infrastructure.
1. Better performance as Google surely has a better server than you have.
As you can all benefits are related to website performance and most likely you read this because you are looking to improve your website performance, am I right?