It is a very handy tool.
Normally, when a program wants to access a specific drive or disk, it will simply try and the OS looks for it. If it is not found, you get a simple request "please insert Foo: in any drive".
This is mostly useless regarding to hard drives etc.
Say you have Deluxepaint5 on your hdd and you double click on an old picture from a floppy disk that refers to Dpaint3:dpaint the system will request the dpaint3: disk.
Assignwedge changes the request to allow an assign of this dpaint3: to e.g. your Work:gfx/deluxepaint5/ folder for this session.
That picture therefore gets opened with dpaint5.