What are Gifts and Faults?
Gifts and Faults are traits that your character has which are not ratable and cannot be assigned a skill value. A Gift would be a positive trait, while a Fault would be a negative trait. Generally speaking, Gifts and Faults represent something inherent to the character, or something learned or acquired which cannot be rated like Skills.
"Arachnophobia", for instance, would be a Fault, while "Underworld Contacts" would be a Gift. The former represents a weakness in the character (a fear of spiders) whereas the latter represents a boon the character has acquired (knows people in the criminal underworld).
As with Skills, there is no definitive list of Gifts and Faults; players should choose Gifts and Faults which match the character conception and would be fun to role-play. Keep in mind that Faults which never affect the character are not actually Faults, and should be disallowed. "Deathly afraid of space travel" in a fantasy game, for instance, is not really a Fault as the character would never be affected by it. Also, do not take Gifts and Faults you are not prepared to role-play; should you take "arachnophobia" as a Fault, you must play out the fear should giant spiders show up in the game.
Which could happen.
Using Gifts and Faults
Depending on the specifics of the Gift or Fault, they can be used one of several different ways in play. Generally speaking, all Gifts and Faults should be discussed with the game master before play, so that both player and game master are on the same page.
Some Gifts and Faults will rely heavily on game master input during play. "Underworld Contacts" or "Hunted by the Mob", for instance, requires that the game master have some idea of who the contacts are, or who exactly is hunting your character; these are things to be worked out before the game starts, but the game master has to be prepared for the character to need something from their underworld contacts, or to have one of the character's hunters show up at an inopportune time.
Similarly, "Never Forgets a Face" or "Photographic Memory" requires that the game master fills you - the player - in with details that you might have forgotten, even if your character hasn't.
Some Gifts and Faults often provide Advantage or Disadvantage; “Agile”, for instance, might grant Advantage when performing tasks that rely on dexterity. Conversely, “Clumsy” would incur Disadvantage when performing tasks that rely on dexterity.