What the sources claim for it
Change, and the conditions under which things are seen indirectly — dream, reflection, night.
History
Where does the Moon come from?
The crescent is the least stylised sign in the set: it is simply the object drawn. Its metal is silver, and its day is Monday, which is still called the moon's day in most Germanic and Romance languages.
In the operative texts the Moon governs visions, dreams, travel by water, theft, and the timing of everything else — the phase of the moon is the second variable, after the planetary hour, that the grimoires refuse to leave unspecified. Its association with change and inconstancy is old enough that Latin lunaticus is already a medical term.
Afterwards
What did it turn into?
Astronomical notation for the Moon and the alchemical sign for silver.
Which texts describe it?
Oldest first, with what each one does with the mark. A mark described in a Bronze Age incantation and a mark first drawn in a seventeenth-century manuscript are different kinds of claim, whatever the shape has in common.
The Key of Solomon (Clavicula Salomonis)
Anonymous; ed. S. L. MacGregor Mathers · 15th-16th c. · Latin and Italian
Pentacles of the Moon for visions, for water and for night work, made in silver.
Read The Key of Solomon (Clavicula Salomonis) in full ↗Cover: Public domain · Unknown author · Wikimedia file page
Nearby
Related marks
Saturn
The scythe. Slowest planet, heaviest metal, and the authority a grimoire invokes for work involving binding, decay and the dead.
Jupiter
A stylised Greek zeta for Zeus. The sign of increase, favour and judgment in one's favour — the grimoires' preferred authority for asking.
Mars
Shield and spear, iron, Tuesday — and, since Linnaeus, the biological sign for male, which is a much later and quite separate job.
The Sun
A circle with a point at its centre — the oldest form in the set, and the one the alchemists used for gold without further explanation.
Venus
Copper, Friday, and every operation to do with love and favour — the counterpart to Mars in the grimoires long before it was in biology.
Mercury
A caduceus drawn as a glyph — the one sign in the set that names a metal, a planet and a god that all behave the same way.