Performance A refers to the highest performance category of air transport aircraft where, if my memory serves me correctly, 'the failure of an engine should not automatically mean the termination of the flight' - or something like that. In other words, the aircraft should continue to fly quite adequately with one engine out. Lower performance categories assume and allow greater penalties on the performance of the aircraft in the event of engine or other systems' failures.
While it's no longer examined in detail in the ATPL exams, you will perforce become familiar with its requirements and ramifications once you start flying perf A aircraft.
Scroggs