The act of entering something — like a building or a highway — is called ingress (antonym "egress"). If you work in a busy restaurant, you have to keep your kitchen ingress and egress straight or you risk a catastrophe with a full tray of dishes.
In astronomy, ingress is also an act of entering, but it is at the beginning of an eclipse when the celestial body first begins to block the sun and cast a shadow. So in a lunar eclipse, ingress is when the Earth begins to pass between the Sun and the Moon, casting its shadow on the Moon. In a solar eclipse, ingress is when the Moon begins to pass across the face of the Sun, blocking it from the sight of observers on Earth.