Can someone explain the differences in simple terms?
All three are JavaScript libraries. All three provide JavaScript component frameworks, if you include JQueryUi with JQuery.
ExtJs is a commercial library with a licensing fee for non open-source development. The upside of this is that ExtJs is very well documented and it has an extensive component set.
JQuery+UI has a limited component set; however, it is free and generally well documented.
Dojo is generally lacking in useful documentation (unless you by some of the books) and it has some cross-browser issues, though it is free.
Not sure what other criteria you are looking at...
Hope this helps.
(obviously some of this is opinion so take it with a grain of salt)
In simple terms:
jQuery is (almost) just a DOM manipulation/AJAX library. It makes it easy to perform async HTTP requests, add/remove elements from the DOM, mess with CSS styles, add CSS3 selector support, etc, all in a cross platform fashion. If you don't need specialized UI components (ie just "enhancing" a "normal" webpage, not doing anything like a desktop style webapp) jQuery is a perfect fit.
Dojo and ExtJS (and YUI which I'd also recommend) however are MUCH broader in scope. In addition to both providing a plethora of UI components - buttons, treeviews, grids, even charts and RSS feed viewers out-of-the-box - they also provide module systems to encapsulate and organize code. In fact, its hard to write ExtJS (or Dojo) code that isn't heavily module based. In short, they're full-blown Javascript webapp frameworks. They make it easy (or at least not mind-bending) to write ambitiously scaled webapps, ESPECIALLY when working with a team.
(Opinion note: jQueryUI, although providing widgets and drag and drop and whatnot, still doesn't give you the real benefits of the afor mentioned frameworks. Also although it carries the jQuery name, its code quality is FAR from jQuery proper's calibur, is full of design oversights and bad decisions and largely lacking test coverage.)