Every week during the Pre-Season, and during each Season, a new set of Challenges become available. At launch, expect there to be seven Multiplayer and seven Zombies Weekly Challenges available every week. Expect something similar when Warzone launches with Season 1.
Every Weekly Challenge awards XP on completion. If you complete five Weekly Challenges for a week, you will unlock a special attachment (Aftermarket Part) or a weapon as a weekly reward. If you earn all Weekly Rewards in a Season, you unlock a Seasonal Cosmetic reward (a Camo, for example).