In many older clocks, the minute hand doesn't attach to the center shaft, but to a "minute pipe" or "minute cannon" that fits over the center shaft. The cannon pinion is the pinion or gear on the minute cannon.
When the minute hand attaches directly to the center shaft, the cannon pinion is the pinion on the center shaft, next to the front plate.
When the minute hand attaches directly to the center shaft, the cannon pinion is the pinion on the center shaft, next to the front plate.