A loose cushion made to fit neatly and sit onto the seat of a side chair to provide a softer landing, to raise the seat height or for aesthetic reasons. A squab can be used over wood, cane or upholstery; it may be boxed, piped, buttoned or not, and cover an inner pad of horsehair, cotton wadding, foam or feather and down.
I’m not sure why a squab, as a squab is a young pigeon, perhaps someone found a squab reminded them of a plump pigeon squatting on a chair seat.