This is the maximum altitude that an aircraft will be able to safely maintain a constant altitude. Problems start occurring as a result of the thinner air. The thinner air creates a difficult situation, there are fewer molecules flowing into the engine, creating less power to turn the propeller. There is less air flowing over the airfoil of the propeller, thus creating less thrust and making it difficult to get those few molecules over the airfoil on the wings to create lift.

An aircraft can climb beyond this service ceiling, but will need a higher airspeed to do so and will not be able to maintain a climb or an altitude above this service ceiling.

A couple of examples of service ceilings:

Cessna 140: 15,500 feet

SR-71 Blackbird: 85,000+ feet