A Focus is a magical tool used by a mage to focus his paradigm to achieve a desired effect via Awakened Magic. Foci are thus items, rituals, and practices that mages use to tap their magical power. A focus may be a totally mundane object or ritual, with no power of its own, but because the mage believes not only in the focus' power but in her ability to use it, the focus opens the door to magic.
However, Foci are not necessary for casting magick, they only make it easier. Mages can transcend their need for a Focus for a short time to express their own Will, but the belief in her own need makes it more difficult for him to do magic unaided. An exception to this are Technomancers: No matter how far an individual Technocrat or Son of Ether travels on the road to enlightenment, he is bound by his paradigm to rely on secondary tools, meaning that, until he reaches the level of an Archmage, he can never surpass his own Foci.