One of the interesting things about Garrosh Hellscream's rise to the position of Warchief of the Horde has been his display of leadership. When he was in charge of the Warsong Offensive, he lead the Horde in battle against the forces of the Lich King's Scourge and the Alliance. Upon returning from Northrend covered in glory, he began his tenure as Warchief by unleashing Horde forces to seize control of Azshara, make inroads in Ashenvale and Stonetalon, and encouraged (one could even say strongarmed) the Forsaken under Sylvanas Windrunner into invading Gilneas in order to secure a port for future advances.
Following this, he orchestrated an elaborate plan to lure the Alliance's leadership to defend Theramore, a plan that nearly succeeded in destroying them with a mana bomb, and has since extended the war to Pandaria where he's dedicated a great deal of the Horde's military resources (and those of factions within the Horde like the Blood Elves) towards finding ancient weapons or things that could be made to serve as weapons, all while sending his Kor'kron to occupy the Echo Isles. In short, Garrosh has been a dynamic leader, and it's hard to dispute that he's made more gains for the Horde during his time as Warchief - both the Dragonmaw and the Blackrock have become powerful Horde allies under Garrosh, Gilneas is heavily contested, the Forsaken have spread across northern Lordaeron, Azshara is firmly under Horde control.