The 'plunger' models had a basic form of suspension where the wheel is held by lugs that slide on vertical rods attached to the frame and controlled by springs either side of the lugs.
This system (as you would expect) can wear rapidly if not lubricated fairly regularly, the rear wheel can then move out of line and the handling of the motorcycle deteriorates, and there's no real damping either.
Swinging arm (UK speak) or swing arm (US speak) was eventually adopted by BSA and most other manufacturers, because it was considered to be a better system.