There are many, many different breathing methods. Some are relatively safe and gentle. Others require close supervision and solid foundational skills. Some are extreme and obscure, stuff that specialists attempt, in order to attain very specific effects and not without risk. And breathing is just one of many different concentration objects you can use.

The people who make the meditation apps are trying to gently coax people into meditation, give them a little taste of it. They know that most people balk at meditation, have all sorts of weird notions and expectations about meditation (but all seem perfectly normal to those people). They know that people like to pretend to have choices, but don't really like to choose. So they chose a fairly gentle method that is not likely to trigger resistance in you. (But I guess the fact that you're asking this on Quora meant that you resisted anyways :-) ).

Breathing in through the nose and out through the mouth is relatively safe (as long as you are not creating a physiological change in your body that leads to panic and anxiety), yet different enough from your habitual breathing so that your mind has to concentrate and be aware of it. If you were sitting in front of a teacher, that teacher can sense when your attention starts wandering off, and gently guide you back to paying attention. As such, you could use a breathing pattern where it is done all through the nose. An app is mechanical, so it won't give you that kind of a feedback.

The important part is learning to pay attention, to become aware of things you normally are not aware of in the present moment -- yet through habit, you have blocked them off. For example, you are reading my words right now, on a computer screen, or maybe a phone or a tablet. You are probably sitting somewhere. Some part of your body is making contact with the ground or with furniture. If you pay attention, you can feel the way the ground presses up against you -- this is the experience of gravity. If you've followed along and actually felt that, you started opening up to the present awareness. My words had guided you there, but once you are there, you don't need these words anymore. The breath is the same way: it's the vehicle chosen by the app makers in an attempt to take you into the present moment. In and of itself, it isn't that special.