Hardened steel punches will easily chip or mushroom the ends of shafts, pins, and bearings. A brass drift is a punch made of solid brass, which is much softer than steel. When you hammer on it, the brass deforms instead of the steel component you are trying to move. This protects critical threaded ends and machined surfaces from being distorted during removal or installation.
Brass is also non-sparking. This makes it the only safe tool to use when working near fuel systems, gas tanks, or combustible vapors in the shop. Over time, the tip of the drift will mushroom and widen from repeated hammer blows. You must grind the mushroomed edges off periodically to keep the tool safe and prevent brass slivers from breaking off during use.