Phasing temporarily causes permanents to be treated as though they don't exist without actually changing zones. A phased-out permanent keeps its counters, attachments, and other relevant relationships until it phases back in.
Clever Concealment can phase out an entire collection of nonland permanents, while Teferi's Protection uses the mechanic as powerful defensive protection. Because cards don't leave the battlefield, phasing doesn't trigger enter- or leave-the-battlefield abilities.