Application scripting is basically a way to extend a program, either automating functions or maybe a series of steps, or adding a new feature. With Word Processors or Graphics apps it can be as simple as recording a Macro (a set of keystrokes).
Vegas offers quite a bit through scripting -- Check out the scripting forum section.
Clarification: In the list of features new in DVDA4, Sony refers to scripting (in the scope of the DVD specs) as "Application Scripting." I think that is what vicmilt is referring to. I wish they'd change the wording, 'cause it does kind of give the wrong impression.
In the context of DVDA it refers to the ability to access the low-level command structure of the DVD- although in the case of DVDA this command structure has actually been somewhat abstracted when compared to the true low-level access that something like DVD Lab Pro provides.
A typical use might be to change the button that's highlighted when you return to a menu from a particular clip. A less typical use (though much more fun) would be to write a simple game for the DVD - the treasure hunt bonus material on the National Treasure DVD is a good example, or the game "SceneIt" is an extreme example of what can be done.
Another way to think about it is thatit gives you access to functionality not available via the WYSIWYG interface.