Compound verbs don't always make a lot of sense, you kind of just have to memorize them. "set off" is also used to me "to start an explosion", so it could be from that. "to start an explosion" became "to start (something)" and also "to start (on a journey)". But really who knows. Edit: Just looked it up in an etymology dictionary, and it seems like the definition meaning "to start" actually came before the definition "to start an explosion". Interesting. http://etymonline.com/index.php?term=set+off

To set off can mean to begin a journey/to depart. For example, "We set off early in the morning for our trip to France."

It's most common use is 'to leave', normally on some kind of journey. Tomorrow we need to set off by midday so that we are on-time for the flight, for example.