It's all about the air
It may sound a silly thing to say, but really singing is all about the air.
The thing is.....singing (in the most part) is a physically 'still' activity. You're not running around a track, you're not hiking. Most of the time when we sing we are in a standing position with little physical movement.
Therefore it feels quite un-natural to take massive deep breaths. But...without it....singing is far trickier.
Imagine you've just run around an athletics track. How are you going to breathe? How deeply? And through your nose, or mouth? I would imagine (if you've run at any speed at all) you will breathe through your mouth, as we can get far more air in through the mouth than sniffing air in. When we are singing although we may not move from our starting point the breathing needs to be as deeply as if we were to reach the end of that track.
We tend to breathe much deeper for the 'power' parts of a song like the big chorus or the high notes. What is less natural is breathing that deeply for the lower or quieter parts of a song. But if we do breathe that deeply in those sections we tend to find that we have much more texture and control in our singing.
When we breathe in a stationary position (i.e. standing or sitting still) we tend to use only about 10% of our lung capacity. You may find that if you breathe deeply for the duration of a full song you feel a slight headrush. This is because your body has suddenly acquired far more oxygen that it has been given prior. This isn't something to worry about, it's just what happens if you give your body more oxygen.
Essentially the more air you have in your body the better your singing will sound. Don't reserve the really deep breathing for the high power bits, if you breathe deeply for the whole song you'll find things much easier.