Learned helplessness is when somebody has been through recurrent negative experiences to the point where they lose the will escape current and future negative experiences which they otherwise could. It is a sense, the breaking of the will.

It was discovered in an experiment with dogs. In the experiment two dogs were being electrically shocked and one dog had the ability to turn off the shock for both of them by hitting a lever while the other dog's lever didn't do anything. The dog that didn't have the ability to stop the shock showed signs of depression and feeling like it didn't have control over the situation.

Then the two dogs were put into an electrical box which they simply had to climb over a low bar to get out of. When it was turned on, the dog that had control in the first test simply got out of the box. The other dog stayed in the box and displayed the same symptoms as it did in the first experiment. They found that rewarding the dog or punishing the dog didn't change its behavior as far as leaving the box and the only way to teach it to leave was to move its legs in a motion that would make it leave and repeating this process a few times until it learned it could escape the box.

So basically when someone has learned helplessness, since they feel like they have no control either way and are use to the situation, they simply give up and allow it to happen to them.