As a musician, performing for a public/paying audience, such as at a bar, concert hall or event. Out refers to 'out in the world' beyond private performances like jams, rehearsals or playing for family and friends. Playing a 'gig.'
I'm in a new band. Rehearsals are going well and I think we're ready to start playing out.
Similar to the phrase "just putting that out there", but it is usually said more as suggestion, particularly when the person saying it lacks confidence that his answer or solution is correct.
A 7 second video of a man holding a camera walking into a room and then being greeted with a preteen playing minecraft and is mad because his PvP skills suck.