An insomniac is someone who can't sleep, someone who stares at the ceiling all night or watches the minutes tick by on the alarm clock or counts sheep into the millions.
Eight hours of sleep per night is considered healthy, but just think of how much more you could get done if you didn't need any at all. If you're an insomniac, though, it's not that you don't need sleep — it's that you can't get any at all. Break down the Latin root word and you get in- and somnus: "not sleep." "Not sleep!" is how you might start talking after several agonizing days of sleeplessness and walking into walls and assigning a name to every sheep that jumps the fence.