 When the axis "precesses" from one orientation to another, the equatorial plane of the Earth (indicated by the circular grid around the equator) moves.The celestial equator is just the Earth's equator projected onto the celestial sphere, so it moves as the Earth's equatorial plane moves, and the intersection with the ecliptic moves with it.The positions of the poles and equator "on Earth" do not change, only the orientation of the Earth against the fixed stars.