Richard Thomas has another Solar Framework Short posted today looking at how to integrate the jQuery Javascript library directly into your Solar application.
When it comes to Jquery integration you have 2 main uses. Calling a php function from a website or calling Jquery functions from php both are done through an XMLHttpRequest.
By extending a jQuery-related controller, you gain some special automatic abilities like automatic json-ification of output data and being able to push out transformations directly back to the browser from a standard javascript call. Check out the post for the complete source code for his example.