|Justice Badges are used to buy different gear as explained on the Exchange page.
You earn 1 Justice badge for doing at least 1,000,000 damage to each boss. Additionally you can earn 4 extra badges by placing in the top 10 in damage on each world boss.
You also earn Justice Badges in Guild Raids. You get 1 Justice Badge for doing 500,000 damage in each guild raid and 1 additional Justice Badge for placing either top 3 or top 5 in damage in the raid depending on the dungeon.