Interact with Target simply does the same thing as RIGHT CLICK does. So if you target the flight master and press your Interact With Target key, it opens the flight path dialog.

When you combine IAWT with "Click to Move," what happens is that if you select an NPC and then press the IAWT button, your character will run over to the NPC and then interact with it.

This is useful for melee characters as it causes your guys to run over to the mob and then interact with (aka ATTACK!) it. For caster classes, it is less useful as you don't want them running into melee all the time.