How is it possible that my computer turned on by itself?

Last night the screen went blank/black, and I could not get the computer to come back, so I turned it off by holding the power button. This morning I was watching tv, and all of a sudden my computer turned on. It booted up exactly as it would if it had been turned off, not like it was in hibernate or stand by, or some other mode that it is technically still on.

What could cause this? Could it be a virus? Some setting I enabled that I don’t realize? Or, do I just have a ghost in my house?

Is it something I need to worry about?