A generator generates a voltage. It will deliver a current when we connect it to a load (such as a light bulb). The current lights up the bulb. However, it also makes it harder to turn the generator.
We have to work harder to keep the generator turning once a current is being taken. The more current we take from the generator, the harder it is to turn it.
This makes sense: we don't get something for nothing. As soon as we get the generator to do work for us, we have to put more work into it. And the more work we get it to do, the more work we have to put in. If this weren't the case, we'd be getting something for nothing. And this would go against the ideas of the conservation of energy.
There is a good physical reason why it gets harder to turn the generator when it is delivering a current: it starts to behave like a motor. The current is flowing in the coils. Therefore there is a force on the coils as though it were a motor. And this force will oppose the motion of the generator and make it harder to turn it. This is the physical origin of Lenz's Law (see page 13). The force on the induced current opposes the force you apply to make the current flow.