You are probably referring to "concentric failure." This is merely training until you cannot the complete the entire range of motion (ROM) of a particular exercise by yourself.
The concentric phase (the positive phase...where your muscles are the prime movers and you are contracting against gravity) will always be the first to fail. In a bicep curl it would be from the elbow extended portion (start) to the elbow flexed postion (finish).
That, however, is just the beginning of intensity...