It seems like they dozed off while driving.
Sometimes even though you're very much awake and alive you need to sleep for a little bit, so you take a nap. But you're not dead! You're totally alive, so let's hope no one thinks you're doing anything but dozing off.
The readings for this word are both kun'yomi readings. You've learned both of these readings by now so you should be able to read this on your own.