Samadhi is both a Pali and Sanskrit word that describes the state of the Citta (heart/mind) when it is collected and settled in the present moment. What it is aware of can be a single object, such as the body, or changing objects, noticing their coming and going.
The body, which includes the body breathing in and breathing out, is an excellent object for the cultivation of Samadhi. As mentioned in the last article, the body can be worked with directly to cultivate calm in and of itself; and, in turn, the body excels in establishing calm in the Citta.
Samadhi arises out of deepening calm (Passaddhi in Pali), particularly as both the body and the Citta begin to take on similar characteristics--which they are wont to do, as they are very sympathetic to each other. These characteristics include calm, but also a sense of openness, receptivity, and stillness. Because the body and the Citta are so sympathetic to each other, as characteristics in one deepen, it supports the deepening of those same characteristics in the other--for better or for worse. In this case, it’s definitely for the better as both calm and Samadhi are what is being deepened. This is called mind/body unification and is the hallmark of Samadhi.
In practice, we don’t try to cultivate Samadhi per se. That would most likely lead to striving, tension, and frustration. Instead we practice for calm and let that deepen naturally in the body and in the Citta. As that process organically deepens, those conditions naturally give rise to Samadhi.