If someone is cognizant of something, they know about it and they understand it — not a fuzzy feeling, but a clear, awake kind of knowing. The usual pattern is cognizant of (a fact, a risk, a rule). You will meet this word in law, government, hospitals, and careful American writing: a firm may be cognizant of the danger; a court may be cognizant of the facts. It is a stiff, official word, the sort that belongs in a report, not in a chat with a friend. In ordinary talk people say they know or they are aware. British speakers use it less and often prefer aware. It does not mean “clever” in general; you are always cognizant of some particular thing. Older legal English also speaks of a cognizant authority — the office that is supposed to know a matter and deal with it.