Deep breathing is relaxing because it’s the opposite of something being wrong. When something is wrong, your breathing speeds up so you have the oxygen to deal with it. Long, deep breaths are something you only do when you’re relaxed.
That’s why it’s so relaxing. When you purposely do something you only do when you’re relaxed, it makes you feel more relaxed.
Before it became all about stretching, yoga was mostly about the breath. People have been studying our breath and how it affects us for thousands of years. You can start learning about it right now, by just taking a few deep breaths and paying attention to how you feel.