Sati is a Pali word from Buddhist practice. It is translated as "awareness," but it has a more specific meaning when examined closely. It is a fundamental aspect of meditation as well as Eastern meta-physics. It is really quite simple, but it might seem unfamiliar to a Western audience. I will attempt to describe it in the plainest terms.

Point 1: Consciousness is a subjective experience.
Consciousness is the totality of your experience. It is subjective because you experience it from your own point of view. But delving deeper, we might claim that your experience of all things exist within your consciousness; or in other words, you cannot observe anything outside your consciousness. However, this is not solipsism or nihilism; it does not deny that things exists. It only claims that your ability to perceive and experience things resides within your consciousness, and thus any resulting perceptions or experiences also happen within your consciousness.

Point 2: Consciousness is not the equivalent of mind-body.
We tend to conceptualize our self as a mind and body. It is tempting to equate self with consciousness, and thus to equal mind-body with consciousness. But this is incorrect. (Going further, it is also fallacious to equate self with mind-body, but that is another topic.) If consciousness was the equivalent of mind-body, then it could not include relationships with things external to the mind and body. But the totality of our experience does indeed include those relationships. Thus, consciousness must be broader than mind and body.

Point 3: Awareness (sati) is the relationship between consciousness and mind-body.
Since consciousness is not equivalent to mind-body, they are distinct. But they are not totally separate either; they are all related. Since they are related, we can examine that relationship. What is that relationship? Going back to the first point, consciousness is the totality of experience. So, the relationship between consciousness and anything else is merely your ability to notice, subjectively, that some thing is present within your experience. Sati is the particular awareness of mind-body -- specifically, that mind-body exists within consciousness, not separate nor equivalent.

Conclusion
Following from the above theory, awareness is not internal to the mind. Awareness is not concentration on a particular object, sense, or activity of the mind. Awareness is the act of noticiting what the mind is doing in the present. Sati is the understanding that the mind itself is an object that can be examined within consciousness. Similarly, the body can be examined, and other things too. And extending further, one can examine the relationships of mind-body, mind-other, and body-other. For this act of examining, the mind is the tool, but not the totality.