My understanding of the term:
Where a power signal box / signalling panel / control centre / signalling centre has a boundary with a smaller existing signal box. As the power signal box / signalling panel / control centre / signalling centre will most likely be using track circuit block (or the same but with axle counters), so will part of the area controlled by the smaller existing signal box.
The remaining area controlled by the smaller existing signal box could be Absolute, Electric Token, TCB or other conventional signalling.
Hence to the power signal box / signalling panel / control centre / signalling centre, the smaller existing signal box is a fringe box, as it’s the boundary or fringe between the area controlled by the (newer) signalling controlled by the power signal box / signalling panel / control centre / signalling centre.
As more power signal boxes / signalling panels / control centres / signalling centres etc have taken over, now rather than the fringe being a conventional signal box, the fringe is the adjacent panel/desk of the next power signal box / signalling panel / control centre / signalling centre.
For conventional mechanical signal boxes that are a fringe box, they often will have a fringe train describer (TD) system. This communicates with the main TD system in the power signal box / signalling panel / control centre / signalling centre. This does not apply when two power signal boxes / signalling panels / control centres / signalling centres fringe one another. Instead, the main TD systems communicate directly with one another.