The description of the word you requested from the astronomical dictionary is given below.
aequatio = [Latin] make equal
Equatorial means it has something to do with the equator. In the equatorial coordinate system, positions in the sky are indicated with the right ascension (relative to the vernal equinox) and the declination (relative to the celestial equator). The celesital equator is the extension of the Earth's equator into the sky, halfway between the celestial poles, which themselves are the extensions of the rotation axis of the Earth.