Think of space as being a stage upon which the actors (the particles) are doing their stuff. Only, in this play, the actors actually interact with the floorboards
Since they're actors, they're doing all sorts of things...rushing about, sitting at rest, moving on and off the stage. Even when they're standing still at rest, because of the Uncertainty Principle you can never know whether they're truly at rest or just jiggering around on the spot. That's where your zero point energy comes from. Dark energy is probably either a component of, or in actual fact, the ZPE (we don't know, yet). Or, it could be something else entirely different.