Safe to swipe, or STS for short, is a phrase used to indicate to a viewer that it is safe to swipe either left or right when viewing photos on another's mobile phone.
It is considered extremely poor manners to swipe in either direction without receiving this kind of verbal clearance as one's extremely personal photos of adult relations may be unwittingly displayed to a wider audience than originally intended - and what has been seen cannot be unseen.
Person #1: Check out this pic of a rockin sunset over the desert I took yesterday.
Person #2: Awesome! Hey dude, am I safe to swipe?
Person #1: Don't you ****ing dare!