Anima is a special power in Xenoblade Genesis. According to the reveal, it is described as an energy that flows through the world and its forces. Nintendo's own page does not name it, so the detail below comes from the reveal trailer and surrounding coverage and should be read as early information.
Overview
Early material presents Anima as something fundamental to the setting, a power running through the land and the people and creatures within it. It appears to be the central force around which much of the world's conflict and the protagonist's journey revolve.
Anima and Warfare
Coverage of the reveal indicates that people sought to harness Anima, and that this pursuit ties into the conflict the story sets up. The reveal frames battles as being decided by Anima and by those able to wield it, which positions the power as both a narrative driver and the apparent basis for combat.
Who Wields It
Those who can wield Anima are called Vesselai, powerful warriors trained for that purpose. The protagonist, Eleanor, is shown on a path to become one. The academy Leukos is presented as the place where students train to reach that goal.
A Crystone is shown amplifying a wielder's power over Anima, and the early material describes crystones being set into weapons such as swords. The relationship between Anima, the warriors who channel it, and the stones that amplify it forms the backbone of what the reveal communicates about the world.
What Is Not Yet Known
How Anima functions in actual gameplay has not been detailed. The reveal does not explain how it is gathered, spent, or used in moment-to-moment play, and no combat system has been shown in depth. Those mechanics are deferred until Nintendo shares more.