Phase is primarily a noun meaning 'a stage', or 'an item in a [repeated] cycle'. The moon has phases - new, quarter and full, for example; children go through phases (for example of naughty behaviour) while they are growing up. Gardens have phases of growth through the year.
So the verb 'to phase', which is transitive, means 'to introduce something in stages'. 'The University will phase in the introduction of the new generation of computers over three semesters.' "We will phase the induction process for the new students over three weeks." The earliest uses of phase as a verb are early twentieth century, and are mostly to do with the new technologies of electricity, wireless and nuclear science.