What is morning wood?

Morning erections have nothing to do with dreams of sexy ladies - or sexy men, for that matter.
I had a hard time pointing at the toilet bowl after waking up today, and all I was dreaming of was that I was in a new job and we'd just been hacked. Hardly stiffy material, I know.
Although now that I think of it, the head developer was played by Jake Gyllenhaal.
Now, Jake Gyllenhaal is absolutely not my type, and I appreciate the effort he made in my dream, sporting the shaved head and combats he donned for his role in Gulf war drama 'Jarhead', but he just does not do it for me. Too young I think.
So I'll just go with the 'specific neuroreflexes that are stimulated during REM sleep' explanation, then.