After doing this 21 times (this will take a few days, at the least) you will unlock: You can accept the challenges in the 24 hour period, although you can take as long as you want to complete them. Once it's complete (they're mostly relatively easy, some are much harder than others), press, navigate to 'Orders' in the menu and go over to the completed challenge to accept your reward. You activate a challenge by going to the one you want and holding to accept the challenge. There are 6 daily challenges that will change every 24 hours, and you can only have 3 challenges active at a time.
Challenges are obtained through Major Howard who is in the center of the Headquarters. Something to keep in mind is that there is an achievement to complete 21 daily challenges. You'll be given a full tutorial and walkthrough of Headquarters when you first enter multiplayer. Headquarters is where you do just about everything, from shooting at the firing range, to obtaining challenges and orders, to prestiging your player, and much more.
The newest addition to the Call of Duty multiplayer is the introduction of Headquarters.