He duelled Cairne, went into bloodlust, scratched him with his axe and then thought he killed him in glorious combat. The axe, however, was smeared with poison (unbeknownst to both combatants) and Cairne dies from the poison and not from the wound. When Garrosh learned, he was all "oh they stole my kill" while Cairne's son was like "dude, my father died".