Library licensing
Like jQuery, the jQuery UI library is licensed under the MIT open source license. This is a very unrestrictive license that allows the creators to take credit for its production and retain intellectual rights over it, without preventing us developers from using the library in any way that we like on any type of site.
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. You can build applications on top of the library and then sell those applications or give them away for free. You can put the library in embedded systems such as cell phone OSes and sell them. But whatever you do, leave the original text file with John Resig's name present on it. You can 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 can therefore demand that the users of our software give attribution to us instead of the jQuery team, or pass off the code as our own.
The license is not there to restrict us in any way and is not the same as the kind of license that comes with software that you might purchase and install on your own computer. In most cases, how the library is licensed will not be a consideration when using it. Plugin authors, however, will want to ensure that their plugins are released under a similar license.