When you select an effect from the app, it is immediately reproduced on your Twinkly lights, so you can appreciate the result.
But if you want that effect to stay on, even when the app is closed, you have to touch the "Apply" button at the botton of the app page showing you the effect.
In this way, the light effect will be memorized on the controller, and the app and the smartphone are no longer needed for it to continue to play.
Even if you unplug your Twinkly, when you turn it on again the light effect will be there again.
For more info on the controller, see also What is the controller and why is needed?