The phrasal verb to 'wait up' means not to go to bed until someone arrives. 'Wait up' can also mean to go more slowly so that someone can catch up to you. These uses are more likely to be heard in casual contexts. 

1. I had to stay late at the office and had no idea what time I'd be finished, so I rang my wife to tell her not to wait up for me, and that I'd see her in the morning.
2. Hey guys, wait up! I want to come to the party with you!
3. My mother was waiting up for me when I came in drunk from the pub in the early hours of the morning. She had been worried sick about me all night!

1. Wait up a second, before you go into that meeting make sure you look presentable and have all your notes ready. We can't afford any mistakes!