Phasing isn't what you'd normally call a well-understood mechanic -- see below for phasing's entry in the current Comprehensive Rules.

However, it's still cleaner than the printed wordings of some old cards. In fact, the phasing mechanic has been used to clean up a few Oracle wordings.

 

Oubliette
Consider Oubliette. Oubliette is a very flavorful card: the creature falls in a dark pit and can't be affected until the Oubliette is dealt with. Describing that in Magic terms in the Arabian Nights era was pretty difficult:
Select a creature in play when Oubliette is cast. That creature is considered out of play as long as Oubliette is in play. Hence the creature cannot be the target of spells and cannot receive damage, use special powers, attack, or defend. All counters and enchantments on the creature remain but are also out of play. If Oubliette is removed, creature returns to play tapped.

Um, "special powers"? Enter phasing:

When Oubliette comes into play, target creature phases out. That creature can’t phase in as long as Oubliette remains in play.
When Oubliette leaves play, the creature phases in tapped.

 

Tawnos's Coffin
Much cleaner. Same deal with Tawnos's Coffin from Antiquities:

, : Select a creature in play; that creature is considered out of play as long as Coffin remains tapped. Hence the creature cannot be the target of spells and cannot receive damage, use special powers, attack, or defend. All counters and enchantments on the creature remain but are also out of play. If Coffin is untapped or removed, creature returns to play tapped. You may choose not to untap Coffin during the untap phase.

Now, its Oracle text, using the rules for phasing:

You may choose not to untap Tawnos’s Coffin during your untap step.
, : Target creature phases out. It can’t phase in as long as Tawnos’s Coffin remains tapped. When Tawnos’s Coffin leaves play or becomes untapped, the creature phases in tapped.

Let's hear it for the elegance of phasing!

 

502.15. Phasing

502.15a Phasing is a static ability that modifies the rules of the untap step.

502.15b During each player's untap step, before the active player untaps his or her permanents, all permanents with phasing the player controls phase out. Simultaneously, all objects that had phased out under that player's control phase in. (See rule 217.8, "Phased-Out," and rule 302.1.)

502.15c If an effect causes a player to skip his or her untap step, the phasing event simply doesn't occur that turn.

502.15d Permanents phasing in don't trigger any comes-into-play abilities, and effects that modify how a permanent comes into play are ignored. Abilities and effects that specifically mention phasing can modify or trigger on this event, however. Permanents phasing out trigger leaves-play abilities as usual. (Because no player receives priority during the untap step, any abilities triggering off of the phasing event won't go onto the stack until the upkeep step begins.)

502.15e When a permanent phases out, all damage dealt to it is removed.

502.15f A card that returns to play from the phased-out zone is considered the same permanent it was when it left. This is an exception to rule 217.1c, which stipulates that a permanent "forgets" its previous existence when it changes zones.

502.15g Effects with limited duration and delayed triggered abilities that specifically reference a permanent will be unable to further affect that permanent if it phases out. However, other effects that reference the permanent (including effects with unlimited duration) can affect the permanent when it returns to play. Example: A creature is affected by Giant Growth and then phases out during the same turn. If the creature phases back in somehow before the turn is over, it won't get the +3/+3 bonus from the Giant Growth because its effect has a limited duration.

502.15h Phased-out cards "remember" their past histories and will return to play in the same state. They "remember" any counters they had on them, any choices made when they first came into play, and whether they were tapped or untapped when they left play. They also "remember" who controlled them when they phased out, although they may phase in under the control of a different player if a control effect with limited duration has expired. Example: Diseased Vermin reads, in part, "At the beginning of your upkeep, Diseased Vermin deals X damage to target opponent previously dealt damage by it, where X is the number of infection counters on it." If Diseased Vermin phases out, it "remembers" how many counters it has and also which opponents it has previously damaged. When it phases back in, it will still be able to target those opponents with its upkeep-triggered ability.

502.15i When a permanent phases out, any local enchantments or Equipment attached to that permanent phase out at the same time. This alternate way of phasing out is known as phasing out "indirectly." An enchantment or Equipment that phased out indirectly won't phase in by itself, but instead phases in along with the card it's attached to.

502.15j If a local enchantment or Equipment phased out directly (rather than phasing out along with the permanent it's attached to), then it "remembers" the permanent it was enchanting or equipping and returns to play attached to that permanent. If a local enchantment phases in and the permanent has left play or is no longer legal to enchant, the enchantment returns to play and then is placed in its owner's graveyard afterwards. This is a state-based effect; see rule 420. If an Equipment phases in and the permanent has left play or is no longer legal to equip, the Equipment returns to play and then stays in play, not equipping anything. This is a state-based effect; see rule 420.

502.15k Permanents that phase in keep the same timestamps (see rules 418.5d and 418.5e) they had when they phased out. This doesn't change the fact that the permanents phase in simultaneously, however.

502.15m A permanent that phases in can attack and tap to play abilities as though it had haste. This applies even if that permanent phased out and phased back in the turn it came into play. The permanent remains able to attack and tap to play abilities until it changes controllers or leaves play.

502.15n A spell or ability that targets a permanent will resolve normally with respect to that permanent if the permanent phases out and back in before the spell or ability resolves.

502.15p Multiple instances of phasing on the same permanent are redundant.