They're cheap (200 souls!), require no effort to use, and they greatly increase the frequency that Darkmoon players can invade the world of the Darkwraith and other invaders to seek vengeance upon your foes! Want to see more PvP action in general? Are YOU a Darkwraith or enjoy invading other worlds using the Red Eye Orb, Cracked Red Eye Orb, and Cat Covenant Ring? Then this is good for you too! Invaders who want action will WANT other players indicting them as often as possible.
What does an indictment do?
Indicted players receive Sin, and their names end up in the Book of the Guilty. This allows Darkmoon Covenant members to invade their worlds and kill them in the name of vengeance. It means players who kill other players will get invaded by Darkmoon more often, and it means those seeking vengeance will indeed receive it more often when indictments are used.
How to Buy Indictments
(Minor early game spoilers ahead.) After you have beaten the first Gargoyle boss, you climb a belltower and ring the first bell. After climbing back down, an individual named Oswald of Carim will be there, greeting you with open arms. He sells indictments. Buy a whole bunch (10 or more) and you're set!
How to use Indictments
When you are killed by an invader while you have an indictment in your inventory, you will be asked if you want to indict the player. Do it! That's it. You're done, and you've helped the Dark Souls community grow larger and more active by doing so. (You only require 1 indictment in your inventory, it is re-useable.) When a player is indicted, they gain 1 point of sin. When they are killed, they lose 1 point of sin. This is why it's important to always be indicting invaders at every chance.
Hand Indictments out like candy!
Indictments are extremely cheap (200 souls per indictment.) Buy a surplus of them and hand them out when engaged in jolly cooperation, or even drop them for the host when you invade their world.
Better the community, and better the game. Buy Indictments.
Other notes; (Thanks! via /u/CZTHIZZKID on Reddit) - A large portion of players who invade do it in an area where they have beaten the boss (to stop people invading them from canceling their own invasions). Players who mostly host in an area don't usually have sin. [This is one reason Darkmoon invasions are hard to achieve.] - Losing to a Darkmoon invasion removes a point of sin. Unless they have tons of sin stacked up, this is another reason why it's hard for Darkmoons to get invasions.