An arm-swinger is someone who swings their arms widely while they walk. People who swing their arms widely while they walk are generally over-weight, and tend to walk slowly. It is likely that a wide arm-swing is needed to counter-balance their large body mass while walking.
Arm-swingers are most notable when they walk in the middle of a busy sidewalk or corridor, thus inhibiting the ability of faster, non-arm swinging pedestrians to pass them. This can lead to great frustration and general deriding of fat people when one is in a hurry.
I would have just made my train today, but I got stuck behind a fucking arm-swinger when I was walking to the station.