The event dispatch thread is a special thread that is managed by AWT. Basically, it is a thread that runs in an infinite loop, processing events.
The java.awt.EventQueue.invokeLater and javax.swing.SwingUtilities.invokeLater methods are a way to provide code that will run on the event queue. Writing a UI framework that is safe in a multithreading environment is very difficult so the AWT authors decided that they would only allow operations on GUI objects to occur on a single special thread. All event handlers will execute on this thread and all code that modifies the GUI should also operate on this thread.
Now AWT does not usually check that you are not issuing GUI commands from another thread (The WPF framework for C# does do this), meaning it’s possible to write a lot of code and be pretty much agnostic to this and not run into any problems. But this can lead to undefined behavior, so the best thing to do, is to always ensure that GUI code runs on the event dispatch thread. invokeLater provides a mechanism to do this.
A classic example is that you need to run a long running operation like downloading a file. So you launch a thread to perform this action then, when it is completed, you use invokeLater to update the UI. If you didn’t use invokeLater and instead you just updated the UI directly, you might have a race condition and undefined behavior could occur.
Wikipedia has more information
Also, if you are curious why the AWT authors don’t just make the toolkit multithreaded, here is a good article.