So here you have two definitions of a blue moon but the one for a calendar blue moon does not describe the true meaning of a blue moon. Here's why:
The moon plays a large role in astrology and astrological phenomena. The position and phase of the moon influences the other aspects of astrology, including sun signs and planetary movements. In fact, the moon influences other aspects of astrology as a whole.
We live in a Cosmic "shooting gallery". Objects inhabiting our Solar System have been profusely and mercilessly blasted by showering asteroids and comets for billions and billions of years. However, planets and large moons have their way of smoothing away the scars--their strong gravity pulls them into a nice ball-like spherical shape. Furthermore, some of these larger spheres possess sufficient internal heat to cause flows of fiery lava and other volcanic features that can fill in the scars of impact craters. A few such large bodies are blasted by strong winds and pouring rains, which also erode away the pockmarks left on their surfaces by showering impactors.