The lunar standstill involves some difficult 3D reasoning so I tried to build a model. You can see the Equator drawn in black on the tennis ball. I've added the axis of the Earth sticking out of the North Pole. Here the Earth is shown upright but actually it is tilted at 23 degrees to the plane that contains the Sun and the other planets. So I've added that plane in clear plastic and tilted it at 23 degrees to the Equator. The Sun appears to do a circle around the Earth. I've drawn it on. It is called the Ecliptic. The Moon takes about 4 weeks to go round the Earth. It appears as a blob of putty on a wire. It is not on the ecliptic. It's orbit is tilted by another 5 degrees.
This is the situation at a lunar standstill. Notice how far above the Equator the putty Moon is - the Moon will appear very high in the sky.
It takes 2 weeks for the Moon to reach the other side of its orbit. Now notice that you are having to look down through the ecliptic so the Moon will appear very low in the sky. This is essentially a lunar standstill - that in 2 weeks the Moon goes from its highest possible to lowest possible position (when viewed looking due south from us).
But the orbit itself doesn't stay still. In the same way that a spinning top goes round in an arc whilst continuing to spin, so the orbit twists - it's called precession. It takes 18.6 years to get back to the position shown in the earlier photographs.
