How the moon phase is calculated
The Moon repeats its phases every 29.53 days (one synodic month) as it orbits Earth. The phase shown above is derived from the elapsed fraction of that cycle since a known new moon in January 2000 — the same almanac method, accurate to within about a day. The illuminated fraction you see is the portion of the Moon's Earth-facing disc catching sunlight right now.
Why 'moon phase today' changes every night
Because the Moon moves about 12 degrees along its orbit each day, the illuminated sliver grows or shrinks visibly from one evening to the next. From new moon (0% lit) to first quarter (50%) takes roughly 7.4 days; a full moon arrives about 14.8 days after new moon, and the second half of the cycle mirrors the first in reverse.
What people use moon phases for
Photographers plan night and golden-hour shoots around the moon's brightness; anglers and hunters track solunar feeding patterns; gardeners follow traditional planting-by-the-moon schedules; and astronomers simply need to know when the sky will be dark.