If you are cognizant of what's going on at the table behind you in the lunchroom, that means you know they're plotting to throw peas at your head. If you are cognizant of something, you are aware of or informed about it.
This 19th century adjective derives from Latin cognōscere "to learn." For the English adjective and noun, an older pronunciation with a silent g was in use in legal contexts up until the early 20th century. In law, these terms refer to jurisdiction, or the right of a court to hear a case.