Perks are a variation of the power-up mechanic, but are permanent rather than temporary and are often progressively unlocked through experience points.
The concept of permanent power-ups that are progressively unlocked through experience dates back to the armaments system of the shooter Gradius and action games inspired by it, such as Slap Fight, Contra Force, and Night Slave. In these games, power-up items (such as orbs) work similarly to experience points and are obtained by destroying enemies. Once you have enough, you can choose from a selection of permanent abilities, and the more power-up items are obtained, the more abilities become accessible, much like perks.
Fallout coined the term "perks" and introduced the concept of adding perks to your character in a role-playing game. Each time you leveled, you were allowed to choose a special buff or ability to apply to your character. More notable ones were "Mysterious Stranger," which by chance a person will come and help you fight in random encounters. And "Slayer," which turns all your hand to hand combat attacks to criticals.
A similar mechanic appeared in Capcom's Onimusha and Devil May Cry series of hack & slash games, where orbs or souls work similarly to experience points. Every time the player character levels up using these orbs or souls, they are given a choice of permanent power-ups or abilities to choose from, much like perks. Another similar mechanic is incorporated in the sphere grid system of Final Fantasy X, where a player character gets a choice of different buffs and abilities to choose from using the skill points they acquire.
Call of Duty 4: Modern Warfare took this idea and ran with it, implementing a number of different perks into their multiplayer component, and continued to expand their use in Modern Warfare 2. These perks include things like increased hip-fire accuracy, longer sprint times, and increased bullet penetration.
The success and popularity of the Call of Duty multiplayer caused other games to follow suit. Uncharted 2 implemented "boosters" into their multiplayer component, and Bad Company 2 allowed a loadout slot for things like magnum ammunition or increased explosive damage. The combat racing game Blur has three "Mod" slots, each one a perk for the player for things such as better shields, easier to pick up power ups, and more damaging attacks.