As a motor coil spins in a magnetic field, it effectively is the same as a generator, that is a conductor coil cutting through magnetic field lines. Thus an emf is induced n the coils. Lenz law states that the direction of the induced current will be such as to create a magnetic field that opposes whatever is causing the induction. In this case the forward current (say A to B) is causing the coils to rotate through the magnetic field as per the motor effect, so the induced current (back emf) will be in the opposite direction (B to A) to attempt to "cancel" out the forward current. Thus say a motor with 5 Amps in its coils at zero speed will have less current while spinning at speed, as the 5A forward current is offset by about 4A backwards current resulting in a nett forward current driving the motor of say 1A..
The answer to CSSA2011 Q 11 is fairly straight forward. The additional load will cause the motor to slow down; this decrease in speed of the coil cutting the magnetic field lines means less emf will be induced (emf is proportional to rate of change of flux) so less back emf will be created. This means instead of producing a back current of 4A (as above) then only say 2A of back emf will be opposing the 5A of forward current leaving a nett forward current of 3A. This means an increase in forward current so the motor will pick up more torque.
