In order to run and start the pistons must be able to compress the air drawn into the cylinder sufficiently to get the correct air to fuel ratio needed to start and run. If an engine has extremely low compression you will hear the starter motor spin it very quickly or you will feel little resistance on the pull cord.
A compression test is a good way to check the general health of an engine. In this video I do one on a Yamaha 50HP four stroke. Around 120 PSI is good; if the compression is much lower, or varies a lot between cylinders, there's not much point looking at other problems until that's fixed. Low compression can come from worn piston rings, a blown head gasket or, on a four stroke, valves that aren't seating properly.
A leak-down test on the same motor, to find out where the compression is going. It points to a burnt exhaust valve on cylinder one, and maybe two.
