You "meet a challenge" if, at the beginning of the end step, you've fulfilled the conditions put forth in the rules text. When you meet a challenge, it goes to your Command Zone.
The number at the bottom of the challenge represents the number of Victory Points it gives you when you fulfill it. A player with 10 Victory Points wins the game. These are easily references by observing the Challenges in a player's Command Zone.
This is probably a bad idea. It was inspired as I was thinking about the Luck Counters/Victory Counters suggestion over on Vote 2 - Bottom up ideas. I actually like that idea better, but I can't just let an idea fade away.
Note that this particular design isn't necessarily any good. It's just here to convey the idea of Challenges.

I'd side with all the comments that we don't need yet another life total.

Problem is, you kinda naturally want "Gain life" and "do damage" as conditions; which makes them also seem pretty odd as rewards.

Quest counters were Wizards' official attempt to play in this space. I kinda agree that making the reward be a sigil rather than an enchantment that's easy to clear out even once reached has value, though.

But if you put stuff in the command zone, I immediately start wondering about answers to stuff in the command zone...