When you turn your key, the key passes "Running" position first, at which point, full power is supplied to the headlights. The key then goes to "Starter" position, at which point starter engages. Starter draws a lot of current, which results in a battery voltage drop (due to battery's internal resistance). Because of that, lights grow dimmer. Once you let go of the key, releasing it back to "Running" position, the lights should go back to being bright again.