Dual licensing is usually about removing as many licensing barriers from using your software as possible.
Roughly the free software world splits into GPL and BSD style. GPL being about viral freedom, BSD being about totally free use. Dual licensing your software both GPL and BSD eliminates licensing from consideration of use. You just use whichever one fits your style. This can stop licensing wars before they start. There is no question of whether your project is GPL compatible, you declare it up front.
The advantage of dual licensing comes out when you start bundling software together. Can GPL'd software be bundled in a BSD licensed project? What about vice-versa? These are difficult questions and dual licensing makes them go away.
Dual licensing a project as both GPL and BSD defangs the GPL. Its viral freedom clauses are effectively unenforceable because the user can simply use it under the BSD terms. Depending on which side of the Free Software fence you sit this is a good or bad thing.
Finally, dual licensing causes some issues when pulling in code from other projects. You must make sure that the code you're copying qualifies for both licenses. Generally when copying code it has to qualify for the more permissive of the two licenses. JQuery cannot pull in GPL licensed code, or they'd be violating the GPL by offering GPL code under the more permissive MIT license. They can pull in MIT licensed code, since you can redistribute MIT licensed code under the GPL. They may not be able to pull in new BSD licensed code since the MIT license does not have a "no endorsement" clause, and is thus more permissive, but likely nobody really cares about that clause.
That said, I Am Not A Lawyer.