Like jQuery, the jQuery UI library is dual licensed under the MIT and GPL open source licenses. These are both very unrestrictive licenses that allow the creators of the library to take credit for its production and retain intellectual rights over it, without preventing us as developers from using the library in any way that we like.
The MIT license explicitly states that users of the software (jQuery UI in this case) are free to use, copy, merge, modify, publish, distribute, sublicense, and sell. This lets us do pretty much whatever we want with the library.
The only requirement imposed by this license is that we must keep the original copyright and warranty statements intact.
This is an important point to make. You can take the library and do whatever you like with it. Build applications on top of the library and then sell those applications, or give them away for free. Put the library in embedded systems like cell phone OSs and sell those. But whatever you do, leave the original text file with John Resig's name in it present. You may also duplicate it word for word in the help files or documentation of your application.
The MIT license is very lenient, but because it is not copyrighted itself, we are free to change it. We could therefore demand that users of our software give attribution to us instead of the jQuery team, or pass off the code as our own.
The GPL license is copyrighted, and offers an additional layer of protection for the library's creators and the users of our software. jQuery is provided free and open source and the GPL license ensures that it will always remain free and open source, regardless of the environment it may end up in, and that the original creators of the library are given the credit they deserve. Again, the original GPL license file must be available within your application.
The licenses are not there to restrict us in any way and are not the same as the kind of license that comes with software you might install on your computer. In most cases, how the library is licensed will not be a consideration when using it.