In World of Warcraft: The Burning Crusade, Blizzard introduced Badges of Justice. For the first time, defeating bosses in heroic dungeons and raids would reward you badges that could be redeemed for epic gear. This instantly became a huge boon to raiders looking to fill gaps in their armor sets, as well as more casual players looking to obtain epic level gear without the committment of raiding. Wrath of the Lich King introduced several tiers of Emblems that served a similar purpose, but eventually this currency system was scrapped and replaced with two types of points: Justice Points and Valor Points.
How To Earn Valor Points
Valor points are earned by completing random heroics, and defeating raid bosses. You can stockpile up to 4000 valor points at a time, though there is a weekly cap of 980 valor points that can be earned.
What You Can Buy With Valor Points
You can purchase several higher tier epics with Valor Points (currently item level 378 as of the writing of this article). The valor bracers are Bind on Equip and can be sold on the auction house or traded to other players.
How To Earn Justice Points
Justice points can be earned by completing random regular dungeon runs, and defeating high level Cataclysm dungeon bosses on regular mode, as well as any Cataclysm dungeon boss on heroic mode. The weekly level 80 raid quest in Dalaran also provides a few justice points. Additionally, you can trade 375 honor points for 250 justice points at the Honor Trade Goods vendor in your faction's capital. There is no limit on how many justice points you can earn each week, though there is a cap of 4000 that you can hold at one time.
What You Can Buy With Justice Points
Justice points can be used to purchase entry level epics (item level 359) and heroic level blues (item level 346). That includes chest, legs, and glove Tier 11 pieces, as well as Bind on Equip boots for all classes. You can also purchase bind-on-account heirloom armor, weapons, and trinkets at the Justice Heirloom vendor. Lastly, your justice points can also be traded for honor or various trade goods at the Justice Trade Goods vendor.
Where To Spend Your Points
The justice and valor vendors are located in Old Town, Stormwind for Alliance and behind Grommash Hold in Orgrimmar for Horde.