cognizant
Aware of something and clearly understanding it.
To be cognizant of something means to be aware of it or to recognize that it exists. When you're cognizant of your friend's feelings, you notice and understand what they're experiencing. When a teacher is cognizant of different learning styles in her classroom, she recognizes that students learn in different ways.
The word suggests a thoughtful kind of awareness that goes beyond vaguely noticing something. If you're cognizant of the rules before playing a new board game, you've taken time to understand them. If you're cognizant of the time while working on homework, you're keeping track of it and adjusting accordingly.
You might hear someone say they're not cognizant of a problem, meaning they didn't realize it existed. A basketball player who isn't cognizant of where her teammates are positioned might make poor passes. Being cognizant means paying attention and truly understanding what's happening around you, which helps you make better decisions. When you're cognizant of something, you know it in a clear, conscious way.