What is the cause of my fork wobbling when applying the front brake?
There are a number of things that could contribute to such a feeling.

You don't mention the type of brakes you have, but disc brakes can contribute to such a feeling since there is some flex between the breaking point (the disc/caliper) and the contact point (the patch of tire touching the ground).  If you have a "flexy" wheelset, this may be something to get used to.  If the brakes are not adjusted properly or are loose, it's possible your disc caliper is moving as well.

Your headset could also be loose, meaning the steertube is moving around inside the frame and should not be.  A headset adjustment may fix this problem, if none of the components are damaged.

Finally, if you have a suspension fork, it's possible you are misinterpreting some suspension compression as an issue (it isn't).  However, it's also possible (with a suspension fork) that the upper and lower are poor fitting and you are experiencing movement that you shouldn't.  

Without more information and specifics, your question won't have a firm answer.