When your up early in the morning, for example for an 8 AM class and you have a boner that won't go away because your wicked tired and keep daydreaming sexual things. This shouldn't be confused with morning wood, because morning wood usually results from having to take a piss, and you have it as you wake up. The tired boner occurs when your wicked tired and wicked bored after you've been up for atleast an hour.
"This sucks dude this econ class is so boring and I'm so tired."
"I know dude I have a raging tired boner and I keep picturing Shannon Elizabeth sitting on my lap naked."