"jQuery is a fast and concise JavaScript Library that simplifies HTML document traversing, event handling, animating, and Ajax interactions for rapid web development. " http://jquery.com
jQuery is a modular JavaScript Library.
jQuery UI provides scripts for interactions like drag-n-drop, and UI widgets, demos can be found here
scrip.aculo.us (http://script.aculo.us) is a set of JavaScript libraries that enhance the user interface of your web sites.
It contains a visual effects engine, a drag and drop library and AJAX-based control elements like AutoComplete, Sliders and more.
It is an extension to the Prototype-Framework (http://prototypejs.org). You can add both to your web site like this:
<script src="javascripts/prototype.js" type="text/javascript"></script>
<script src="javascripts/scriptaculous.js" type="text/javascript"></script>
To see some demos of what can be done with script.aculo.us go to:
http://madrobby.github.com/scriptaculous/demos/