Phase
Also called: lunar phase, waxing, waning, crescent, gibbous, first quarter, last quarter.
How much of the Moon's (or a planet's) sunlit side we can see: crescent, quarter, gibbous or full.
The Moon is always half-lit by the Sun; its phase is how much of that half faces us. From new Moon it waxes through crescent and first quarter (half-lit) to gibbous and full, then wanes back. A full cycle takes 29.5 days.
Venus and Mercury show phases too, because they orbit inside Earth's orbit — Galileo's observation of Venus's phases helped prove that the planets go round the Sun.
At the eyepiece
The best lunar views are not at full Moon, when shadows vanish, but a few days either side of the quarters.
In AstroPilot
AstroPilot draws the Moon's phase on Tonight, the sky chart and the Moon's page; the planets' pages show Mercury's, Venus's and Mars's.