As commander of the Rebel Fleet, Ackbar has one of the most important and demanding jobs in the Alliance. The fleet is the Rebellion's most valuable asset and its most important tool to challenge the overwhelming might of the Empire. Admiral Ackbar was the natural choice for fleet commander.
Beyond the qualifications of his great skills and sterling character, Ackbar is a symbol to the rest of the galaxy: a symbol that the Alliance is fighting for everyone, no matter what their background or origin. The Empire, in contrast, has made discrimination against non-humans a longstanding policy.
Ackbar proved his competence while commanding the Shantipole project, which added the valuable B-wing fighter to the Alliance's arsenal. He was also extremely influential on his home planet and was largely responsible for that planet's decision to supply their precious Mon Calamari Cruisers, the cornerstones and largest vessels of the Rebel Fleet.
Although widely recognized as a fine tactician, it is his organizational and administrative abilities that make Ackbar an outstanding leader. He is known for being rather conservative in battle strategy, but this aspect of his personality is counterbalanced within the fleet's command structure by the innovative impetuosity of his young officers and the aggressive nature of General Madine.
A case in point is the Battle of Endor. When the Death Star surprisingly went operational and began systematically destroying the Rebel Fleet's most powerful vessels, Ackbar's first instinct was to call off the attack. But Lando Calrissian pleaded with him to continue by engaging the Imperial Star Destroyers, in the hope that the Death Star wouldn't be able to open up on them without hitting Imperial ships.
For all of his conservatism, Ackbar saw the logic in Calrissian' radical plan and acted accordingly. The gamble paid off.
The battle over Endor proved to everyone that Mon Mothma's choice for command of the fleet was perfect. It was the Alliance's shining moment, and Ackbar deserves much of the credit.