Increase the volume, speed, intensity, or flow of, as in Turn up the air conditioning; it's too hot in here. [Late 1800s]
Find or be found, as in She turned up the missing papers, or Your coat turned up in the closet.
Appear, arrive, as in His name turns up in the newspaper now and then, or Some old friends turned up unexpectedly. [c. 1700] This usage gave rise to turn up like a bad penny, meaning that something unwanted constantly reappears, as in Ken turns up like a bad penny whenever there's free liquor. Bad here alludes to a counterfeit coin.
Fold or be capable of being folded, as in I'll just turn up the hem, or He preferred cuffs that turn up. [c. 1600]
Happen unexpectedly, as in Something turned up so I couldn't go to the play. Also see the following idioms beginning with turn up.