The adverb off means away or distant. You might run off from the dinner table after an argument with your family about what to watch on TV later.
You might dash off, moving away from where you started, or turn off your original route during a trip. There are several other meanings of off, including "not scheduled," as when you're off work, and "not running," like when you turn off your leaf blower so you won't scare your neighbor's dog. Food can be off too, when it's gone a little bit bad or spoiled. The colloquial "to off someone," or kill them, is from 1930.