Here my own experience with headspace.
I was meditating for some time, but I felt like I wasn't making any progress. I know the point is not to aim for progress, but I was and it was discouraging. So headspace helped me back on track.
I really liked Andy's voice and the guided session helped me see meditation in a different light. He uses all these metaphors to make you realize that thoughts are constantly passing, that you shouldn't judge yourself for getting caught up in a thought pattern.
I would say that the biggest advantage to meditation apps is that they distract you from your own thoughts and draw your attention to certain topics. They can also teach you how to relax when you're finding it hard to do that by yourself.
Also, I want to add, I stopped using headspace, because I didn't feel the need for guidance at some point. Actually, I felt it was distracting me, so I returned to meditation without any guidance or other devices.