A competition timer means you must complete the workout as close to the routine as possible.
For example, for a guided routine with competition timer enabled, if the workout is 30 seconds of push-ups, only the push-ups you complete in the 30 seconds count towards your score. Completing any extra reps after the time elapses are not counted.
Similarly, if the routine calls for 30 sec of rest. As soon as your rest time is up, the next set will begin.