At the end of December (in the northern hemisphere) we see the Sun rise in the south-east to set in the south-west, describing a smallish arc in the sky (at noon, the Sun is fairly low on the horizon). But the following days, all the way to the end of June, it will rise a bit further north every day all the way to the north-east and similarly set further north-west, describing a much larger arc in the sky (at noon the Sun reaches the Zenith). We see the sun rise higher during the first half of the year and then lower in the second half of the year. The Moon has exactly the same course but its cycle last 27 days, 7 hours and 43 minutes.
To resume, the ascending and descending Moon is linked to the movings the moon has in the sky.
The Moon position on the 20th and the 21st.
Nothern and Southern hemisphere
In the southern hemisphere, the reverse takes place. While in the sky of northern hemisphere we see the Moon ascends, we see the moon descends in the sky of southern hemisphere.