Injury occurs when a hero is under-levelled and/or under-equipped for a certain quest.
While injured, the hero will be unable to be sent on other quests.
It has been confirmed by CloudCade Tadaaah that over-equipping heroes, therefore raising their power, to more than recommended actually reduces the chance of injury. It is said that because of the way power gets rounded up, even if a hero has the recommended power for a certain quest, they may actually be a couple of hundred short. It is therefore suggested to give a hero a few hundred more power than recommended, in order for them to actually have the correct amount and therefore reduce the risk of them returning injured.