"Concentration," as used in meditation circles, is a translation of the Pali word samadhi. As such, it is important to define it precisely; it has been pointed out that "concentration" is not the best word to render samadhi, but we use it here because it has been almost universally adopted by the English speaking dharma world.
In the context of meditation, concentration refers to "non-distractedness." It is the condition of resting the mind in or around the object(s) of awareness. But this does not mean that concentration always refers to a tightly focused mind. Samadhi is a broad term which encompasses not only pinpoint, one-pointed focus, but also a wide and diffuse awareness. In fact, concentration develops through various stages, beginning with a very tight focus and moving toward a wider focus as it deepens. One mistake that meditators often make is attempting to maintain a tight focus even after the mind is ready to move on to a more diffuse way of resting in the object of awareness. For a down-to-earth explanation of how concentration develops, read this essay. If you think of the zoom lens on a camera, with the infinitely variable capacity to zoom in tight or to pull out to a wider view, you can get the sense of this. But in the context of the mind, it's possible to zoom out much wider than the widest camera lens. The highest states of concentration can have a panaramic scope that excludes nothing within the field of experience.
Concentration is tremendously important to the development of both [jhana | samatha jhana] and [insight], because without concentration the mind just flutters from one object to the next, never settling down, and never gaining enough stability to see into the true nature of reality. It is for this reason that concentration is identified in the [Theravada] Buddhist tradition as one of [The Seven Factors of Enlightenment].