While a permanent is phased out, it's treated as though it doesn't exist. It can't be the target of spells or abilities, its static abilities have no effect on the game, its triggered abilities can't trigger, it can't attack or block, and so on.

Phasing out doesn't cause any "leaves the battlefield" abilities to trigger. Similarly, phasing in won't cause any "enters the battlefield" abilities to trigger.

Any one-shot effects that are waiting "until [this] leaves the battlefield," won't happen when a permanent phases out.

Any continuous effects with a "for as long as" duration ignore phased-out objects. Any such effects will expire if their conditions are no longer met after ignoring the phased-out objects.

Each Aura and Equipment attached to a permanent that's phasing out also phases out. They will phase in with that permanent and still be attached to it. Similarly, permanents that phase out with counters phase in with those counters.

Choices made for permanents as they entered the battlefield are remembered when they phase in.

A permanent phased out by The Doctor's Childhood Barn phases in during its controller's untap step as normal only if The Doctor's Childhood Barn is no longer face up. (This situation may occur in rare instances if the delayed triggered ability that would normally cause those permanents to phase in immediately is countered.)