A current carrying conductor within a B field experiences a force (by the motor effect), which gives rise to the torque in a motor.
When you have many of these conductors (like the many coils in a motor), each of these conductors experiences that force, adding up to give a much larger force and torque. This is why a motor with say 100 coils, has approximately 100 times greater torque than a single loop of wire.
If insulation is damaged in some places, the coils (which are right next to each other) would just short out, so most of the current would just bypass the coil (it would simply travel directly between the two exposed parts), and you'd get a lower torque.
Say all the insulation is worn out: you would effectively just have a huge single loop of wire (not 100 coils). You would no longer have that adding up effect; rather you'd just have one big fat current carrying coil.
You'd also probably have a huge current, which would burn out your wires/connections.