One of the characteristics of motors is that they MUST also function simultaneously as generators.
As soon as a conductor is rotating in an external magnetic field, there will appear an induced e.m.f. in the conductor. OK, so that is the origin of the back e.m.f.
Lenz's Law says that the induced e.m.f. will appear so as to oppose the change that caused it.
Last point that needs to be made is the induced e.m.f. is proportional to the angular speed of the motor, as shown by the graph.
These facts lead to the conclusion that the induced e.m.f. will subtract from the applied e.m.f. so we can expect zero effective e.m.f. when they are equal, and the motor stops accelerating at this point.
It reaches a terminal angular speed, and the motor is no longer experiencing a torque.
Does that help?