Historically, a phylactery referred to a special arm wrapping with a prayer box that contained sutras, divine power and a portion of the wearer's soul. Mages refer to a phylactery as a container for the power to perform magic. Your mage's Avatar exists in the physical plane, invested into an object or place, or possibly imbued into some creature or person (such as his familiar or ally) or even a part of his body. On rare occasions, it may be invested into some nebulous concept, like a bloodline, secret society or a religion. The good news is that this object or creature is now Correspondence Range 0 in regards to yourself, which means you can sense it wherever it is, unless it's shrouded by warding. Teleporting your phylactery ring off your finger or making you drop your phylactery sword is as difficult a feat as teleporting your finger off your hand or forcing you to chop off your own arm. The bad news is that you must be in actual physical contact with your phylactery in order to work magic — even if that physical contact is long distance, like a Virtual Adept linked via modem to the mainframe in his bedroom. Moreover, you need to be very obvious about what it is you're using to perform your arts. If your mage's phylactery is his staff, your mage must wave it grandly during all invocations; if his phylactery is a crown, he must hold his head high and wear the crown everywhere he intends to do magic.
If your mage's phylactery speaks to him as his Avatar, you should also take the Merit: Manifest Avatar. If the phylactery is an object, you should probably take the item as a unique focus. As with any unique focus, a phylactery can be repaired or retrieved if it is damaged, destroyed or stolen.
If your mage is separated from his phylactery, you may roll Perception + Sensitivity to sense the surroundings of where it is, depending on how the phylactery might perceive such things. If your mage's phylactery is animate (as with a cat or horse or severed-but-still-living hand) it will also do its best to find its way back to you, having the same homing sense.
Similarly, if your mage's Avatar is invested into a place, such as the Royal Forest of Dean or San Francisco, transporting him away from it, at least by magical means, is about as difficult as teleporting a city block to Istanbul. If he is removed from his phylactery by mundane means, his homing sense will lead him back. In cases where a phylactery is a place, the Avatar fuses with the City Father of that area. That is to say, your Avatar becomes one with the totem spirit of that particular region — Emperor Norton in San Francisco, Belle in Atlanta, a certain highly trademarked mouse in Disneyland. You should take an Avatar rating on par with the importance of your character's bailiwick. Wild places such as forests, deserts, rivers and even oceans can be linked with the same way, although your character must be in them or on them to work his magic. The Pacific Ocean is huge, but if that's your mage's phylactery, his connection to it ends once he sets foot on dry land. Generally speaking, it's not the size of an area that's important so much as the identity. The Queen of Angels may control most of Los Angeles, but there's a different identity to Hollywood and Malibu.
If your character's phylactery is a place, your Storyteller may also allow your character's magic to work in other places somehow linked to it. A mage with Hashberry for her Avatar could probably work her magic in other parts of San Francisco with raised difficulties the further she got from the Haight, and more powerful Avatars could probably work their magic in foreign lands tied to their spirit.
Finally, if your mage's phylactery is a concept with a physical or temporal manifestation, such as the Roman Catholic Church, Iteration X, the witch's Sabbath or the season of Christmas, you may work magic as long as your character is an accepted part of that institution. The symbols and tools representing it can be destroyed, of course, stripping your mage of his magic temporarily, but they can be replaced.
In cases of identity phylacteries, your mage loses his connection to his Avatar if he is disowned, banished, defrocked, excommunicated or otherwise kicked out. As such, members with this Flaw are intensely loyal. If the organization or other concept is destroyed, the Avatar is destroyed, but an organization cannot be destroyed until all members either die or truly renounce their loyalties. When a concept is your mage's phylactery, his Avatar is the protector or mascot of that concept.
If a mage with a phylactery ever dies, the Avatar may or may not go free, at the Storyteller's option. If it does not go free, the phylactery remains as it is, awaiting the mage to reclaim it in his next incarnation.