What is the point called that the Earth and Moon revolve around in space?

When the Moon's shadow falls on the Earth, that's called a "solar eclipse". There are two areas affected; the area of the partial eclipse, where the Moon blocks only part of the Sun, and the total eclipse, where the Moon blocks all of the Sun's light.

Because the Earth is spinning and the Moon is moving, the area of total eclipse travels across the globe from west to east. This is called the "path of totality". You can see the path of totality displayed on a google Map for any eclipse from 2000 BCE to 3000 AD at the NASA eclipse web site at the link below.