Your footing is a supportive place to put your feet when you climb or balance. Once you find your footing at the top of a mountain, you can look around and enjoy the view.
Your literal footing is what keeps you sturdy, and if you lose that footing, you stumble. Figuratively, your footing is your status or position, especially when compared to other people. So if every student in your class is on an equal footing, it means your teacher gives them all the same amount of attention and treats them fairly.