Both Uses of

phase
in
The Age of Innocence

But, as it was against all the rules of their code that the mother and son should ever allude to what was uppermost in their thoughts, he simply replied: "Oh, well, there's always a phase of family parties to be gone through when one gets engaged, and the sooner it's over the better."
Chpt 5 *

phase = stage (of the development of something)

But my poor child is going through a phase of exaltation, of abhorrence of the world.
Chpt 21 *

phase = a period of time when someone exhibits unusual behavior

Definitions:

(1) (phase as in: a critical phase)
a period of time or a stage during the development of something
(2) (phase as in: she's going through a phase)
a period of time when someone exhibits unusual behavior
(3) (phase as in: phased out over three years)
make a change gradually (phase in = gradually add; phase out = gradually removed)
(4) (meaning too rare to warrant focus)
meaning too rare to warrant focus:

More specialized and less common senses of the word are found in astronomy, physics, chemistry, and zoology. Consult a comprehensive dictionary if you wish to see those. All senses have to do with stages or periods of time.