1705, "phase of the moon, particular recurrent appearance presented by the moon (or Mercury or Venus) at a particular time," back-formed as a singular from Modern Latin phases, plural of phasis, from Greek phasis "appearance" (of a star), "phase" (of the moon), from stem of phainein "to show, to make appear" (from PIE root *bha- (1) "to shine").
Latin singular phasis was used in English from 1660 for each of the aspects of the moon. General (non-lunar) sense of "aspect, appearance, stage of development at a particular time" is attested by 1841. Meaning "temporary difficult period" (especially in reference to adolescents) is attested from 1913.
"to synchronize, adjust the phase of so as to synchronize," 1895, from phase (n.) in the physics sense of "particular stage or point in a recurring sequence of movement or changes" (1861). Earlier as a bad spelling of faze. Meaning "to carry out gradually" is from 1949, hence phase in "introduce gradually" (1954), phase out "take out gradually in planned stages" (1954). Related: Phased; phasing.