A mathematical constant is a special number, usually a real number, that is "significantly interesting in some way". Constants arise in many different areas of mathematics. Constants such as $e$ and $\pi$ occur in diverse contexts such as geometry, number theory and calculus.
What it means for a constant to arise "naturally", and what makes a constant "interesting", is ultimately a matter of taste. Some mathematical constants are notable more for historical reasons than for their intrinsic mathematical interest. The more popular constants have been studied throughout the ages and computed to many decimal places.