try to give a short resume:
the jQuery-stuff was shipped with 2.8 because it was used a little bit in the backend and a few never modules use it. One of the next steps will be, to replace the YUI stuff in the backend with equivalent jQuery.
The decision to use jquery was the easier handling and to give (module)developers an easy to handle framework, without the need to bind the necessary scripts into the modules and give a common base for the jquery framework to avoid trouble with different modules loading their "own" jquery.js
There is per default no jquery functionality for the front end. But you can use all the nice jquery features in your template by calling the main scripts from the include-folder, if necessary add your own jquery-plugins, and so on.
You can do this the conventional way like described on the jquery pages or in a more "expert" way like in the examples from Dietmar.
If I wrote some bullshit, please correct me.