1. To sleep in another person's house as their guest. My son is staying the night at his friend's house tonight. It's getting late, so why don't you both stay the night in our spare room?

2. By extension, to stay the night in someone's bed, with the implication of having sex with them. Are you sure you're ready for him to stay the night? You've only been going out for a couple weeks. Even when I was in my mid-20s, my parents still didn't allow my girlfriend to stay the night with me.