What the time delay does is delays the flow of power to the skimmer by 5 minutes after power has been re-established to the time delay box. If you loose power, once power comes back, the time delay (yellow box) will delay turning on the skimmer for 5 minutes after the power comes back.
This is done so the skimmer does not overflow.
Most people keep the skimmer in the sump but when there is a power loss, water from the tank and plumbing makes its way back to the sump and the water level of the sump goes up. In essence, the skimmer is sitting in much deeper water than usual. When power comes back and turns the return pump on, the water level in the sump slowly goes down as the return pump pushes the water up. If you turn on the skimmer at the same time, since the skimmer is in deeper water, it will start to overflow. But, if you delay the start of the skimmer by 5 minutes, then it will allow the return pump to push the excess water back up to the tank and bring the water level in the sump back to it's normal height. Then the skimmer turns on and you do not have the overflow issues.
Hope this helps.