We're engaged in building your concentration muscle, aka taming the monkey, and we're using awareness of breath to do it. You find and focus on your breath, inevitably get distracted, and then refocus/recover and sustain focus for as long as you can – repeating the process as often as necessary. Over time, your ability to choose where and when you focus will grow, along with your peace of mind.
As we're spending so much time focusing on breathing, we'll come to gain more insight into what's going on with this deep and (usually) unconscious biological process – it's the main thing keeping you alive! Every breath you take buys you another minute of life, until your breaths run out.
There's an unfortunate medical condition which used to be known as Ondine's Curse, where people have to pay attention to their breathing in order for it to happen.
Ondine's curse is one of the most enchanting mythical tales in the field of Medicine. The nymph Ondine was an immortal water spirit who became human after falling in love with a man, marrying him, and having a baby. In one of the versions of the tale, when she caught her husband sleeping with another woman, she cursed him to remain awake in order to control his own breathing. During the 19th century, the rare syndrome characterised by loss of autonomic breath control, while voluntary respiration remains intact, was cleverly named “Ondine's curse”. Nowadays, the term Ondine's curse is usually associated with congenital central hypoventilation syndrome.
Practice as if you had this condition. Does this change your capacity to sustain attention on your breath? Don't lose the sense of ease you focused on yesterday!