
It's full moon during the left animation, our Moon orbits "behind" Earth
(as seen from our solar vantage point). It orbits too high, no eclipse,
just full moon.
The animation on the right shows the new moon 14 days later, which
orbits in front of Earth (between Earthlings and us on the Sun). It orbits
too low, still no eclipse. To Earthlings, our Moon appears in the daytime
sky and since they can't see the lit-up half of our Moon, they miss it
completely in the blue sky. - At best they could see a thin sliver right
before or after new moon.

2 and 4 weeks later our Moon still orbits too high or too low for an eclipse
to occur. But it's closing in.

Now it's eclipse time.
Another 2 weeks later, the left animation shows our Moon during full
moon, as a lunar eclipse occurs. All Earthlings, for whom it would be night,
would see the lunar eclipse.
And after yet another 2 weeks have gone by, the animation on the right
shows a solar eclipse during new moon.
You can see that lunar and solar eclipses occur subsequently 2 weeks
apart.
Check out the
eclipse as seen from our Moon to see that our Moon's umbral shadow
covers only a small path across Earth. That's why solar eclipses do not
occur everywhere on Earth.
Now the cycle repeats itself: Our Moon starts orbiting too high
or too low until after 6 months it again closes in on the Earth-Sun line
and another pair of solar and lunar eclipses take place.