Synodic month
The Moon takes about 29.53 days to cycle through its phases relative to the Sun.
Moon Phase Calculator — Examples
Examples, context and typical uses for Moon Phase Calculator.
Waxing and waning
Waxing means the illuminated portion is increasing as observed from Earth; waning means it is decreasing.
Accuracy
Phase calculations here approximate the mean lunar cycle. Exact illumination and rise/set times require astronomical ephemerides.