When you have cognizance, you have knowledge of something. Your cognizance of the English language is growing with every new vocabulary word you learn. Just don't flaunt your cognizance too much, or your friends might call you a "know-it-all."
Cognizance can be used to refer to more than just school-based learning (like vocabulary words). It can also mean that you have awareness, or notice certain things. Your cognizance of where the exits are located in the movie theater could save your life in a fire. The noun cognizance can also refer to your state of consciousness: "You passed out from the smoke, but when you woke up you had the cognizance to know who you were and where you were."