Plain English Meaning
The highest altitude a twin-engine airplane can still slowly climb after losing one engine. Above this altitude, the airplane can no longer climb on the remaining engine and will begin to drift down.
Full Definition
For a multi-engine airplane with one engine inoperative, the single-engine service ceiling is the maximum density altitude at which the airplane can still maintain a steady climb of 50 feet per minute at the best single-engine rate-of-climb speed (VYSE), with the critical engine failed and feathered, the operating engine at maximum continuous power, and the airplane in a clean configuration at maximum certificated takeoff weight.