Sanskrit/Pali word meaning self or soul, as well as breath. Conceived by Hinduism to be that portion of the Divine within each person, that was passed on from life to life in a form of reincarnation that centered on transmigration. The Buddha taught the doctrine of anatman, that is, the absence of any permanant self or soul.
In particular, what the Buddha rejected was the notion of 1) a permanent 'self' that is changeless through the samsaric cycle (i.e reincarnation/rebirth), and 2) an unseen 'essence of humanity' existing outside the Five Aggregates. The Buddha rejected the first of these in light of his teaching regarding impermanence; he said that if one observed closely the mind and body, one could find no evidence that there was any perceivable entity that existed without continuously changing. The second is rejected by a principle similar to Occam's Razor; if we look at the Five Aggregates, we find no function or capability of the human being that lies outside their scope. Furthermore, by analogy, we know that a table, for instance, is made up of non-table elements; a plane parallel to the floor of some material, and legs roughly perpendicular to the floor of some material. When these elements are all present, no 'essence of table' enters to make it a table; we meerley label the confluence of all these non-table things 'table'. Likewise, when the Five Aggregates are present, there is no 'essence of human' that arrives to bless the proceedings; rather, we call the union of the Five Aggregates a sentient being.
As the Hindu/yogic concept of breath, atman is distinct from the concept of prana, the regular day-to-day breath that we all experience. As breath, atman has a meaning closer to that of an animating force; it is the 'breath of life' of the Christian and other traditions. Through the means of following the breath of the body, the prana, certain Hindu yogic meditation practices seek to put the individual into connection with the atman, the divine breath.