You can also keep up with someone when running. If I keep up with my friend when we're running together, that means that I can run at the same speed as my friend. Yes, sometimes when I spend the night at my friends' house, they keep me up late (cause me to go to sleep later than I should). It is similar to 'stay up'. To stay up is to stay awake instead of sleeping. To keep someone up is to cause them to stay up. I hope that helps!

You might also come across the phrase 'to keep up appearances' - this means to maintain a facade of propriety or prosperity. Related to this is the expression 'keeping up with the Joneses" where the family name Jones just means other neighbours/people generally, not a specific family. It means trying to appear as wealthy as your neighbours.