What is a make or break engine?

A "make AND break engine" is an engine which controls power/speed by making (enabling) and breaking (disabling) the ignition cycle.

In one classic design: One or more large flywheels are attached to the crankshaft. A flyweight governor is also attached to the crankshaft. When the shaft speed slows, the flyweight falls inward, releasing a mechanism which allows the exhaust valve to open. When the piston rises to the cylinder head, the exhaust is pushed out. When the piston pulls back, suction is created. a check valve (one-way valve) in the exhaust closes. That resulting suction opens the intake valve and draw fuel/air mix in. The piston then compresses, ignition occurs, and we get a power stoke. This kicks the crankshaft speed back up. The flyweight pushes out, covering the exhaust valve, and thus blocking further engine cycles. The flywheel, crankshaft, and piston run free, on momentum, until shaft speed slows again, and the process repeats.

This is in contrast to most modern engines, which vary speed/power with a throttle, limiting and increasing fuel/air mix, but keeping the ignition cycle active at all times.