So the OP never got an answer.
The question was posted twelve years ago and the OP has been gone for a long time.
In school, I studied business and theology which makes me unqualified to answer.
Hmmmmm... seems like my kind of thread!
Short answer: He saved Rome from defeat, slavery and possibly extinction while facing (probably) one of the dozen best military leaders in history.
Long answer....
Hannibal had already inflicted defeats upon the Romans at Ticinus, Trebia, and Lake Trasimene. At Trebia, the Romans suffered 75-80% casualties.... over thirty thousand men killed or wounded. At Lake Trasimene, they lost another 30,000 men.... ninety percent casualties! Ninety percent!
Hannibal showed the Romans and all military historians a number of textbook maneuvers... before there were textbooks. First, on his own, he started a war with a superpower that he intended to win. The Carthaginian Senate/Council did not authorize or start the war... it was all Hannibal. Then he took his army from Iberia (Spain), along the Gallic coast, to Italia. When blocked by the army of Publius Cornelis Scipio, Hannibal made Scipio think he went back to Iberia all the while marching his army (including elephants) over the Alps... in late fall/early winter. (Here, I have to say that to get over the Alps, Hannibal had to discard and/or use his wooden siege equipment.) Third, he performed the first (if I recall correctly) recorded account of a general cutting his enemy's supply line to force a battle... the Battle of Trebia. At Trebia, he used a combination of food, temperature, terrain, fatigue, and ambush to destroy Scipo's army. The fifth brilliant move by Hannibal was to lure Gaius Flamminius to Lake Trasimene and then to almost annihilate his army.
The Romans, unlike most societies of any period, refused to surrender. They remembered the sacking of Rome by the Gauls in 390 BC. They remembered the abuses of Tarquinius Superbus. They recalled the heroism of Horatius Cocles and Cincinnatus. They knew the story of how Romulus killed Remus for "invading" Rome. They knew the sacrifices their fathers mad to defeat the Carthaginian navy in the First Punic War. SPQR would not give in to Hannibal.
But to illustrate the effect that Hannibal had upon the Roman Psyche, Roman mothers used the name Hannibal as a bogeyman to frighten their children into obedience... over two hundred years after his death. He was the single greatest enemy the Romans ever faced... therefore, the man who saved Rome must be it's greatest hero.
So the Senate called upon Quintus Fabius to take up the mantle of dictator. Not a dictator as in current times, but a man called to a specific term to fix a national crisis. The Senate gave him a newly formed army... which he realized would be no match for Hannibal's veterans. So he stayed close to Hannibal... close enough to catch Hannibal if he settled down into a siege, but not close enough (as long as they kept moving) for Hannibal to catch.
Fabius stayed close to harass Hannibal's scouts and foragers. At that time, the cities of Italia all had differing relations with Rome. Some were close allies... and they strongly resisted Hannibal. Some were friendly cities with trade agreements... their commitment to Rome varied. Some were conquered cities... their commitment to Rome was forced. But all knew that Rome was ruthless to enemies and traitors. The few cities that did ally with Hannibal played a deadly game.
Fabius knew Hannibal did not have real siege equipment nor the facilities to produce it. He wanted to keep it that way. His military and political strategy (continued friendship to allies and friends and threats to the conquered cities) kept almost all of Italia allied to Rome. This meant Hannibal's army never really got a day off.
Fabius also knew that Hannibal's veterans were trained for war. By not fighting, he let their skills diminish.
Fabius relied upon Roman naval superiority to keep Hannibal from being resupplied in men and equipment.
This was the beginning of the Fabian strategy. And the Senate hated it.
After receiving reports that Fabius let Hannibal out of a trap at Ager Falernus, the Senate called Fabius back to Rome to explain himself. In his absence, Minucius Rufus, the Magister Equitum, severely defeated a portion of the Carthaginians in a skirmish. Since this was the only victory the Romans had over Hannibal since the war began, the Senate made Minucius co-Dictator with Fabius. Hannibal learned of this and set his army up as bait for the newly empowered and over confident Minucius. At Geronium, Hannibal surrounded Minucius and most likely would have annihilated his army if Fabius had not arrived from Rome with reinforcements. Minucius realized his mistake, his pride, Hannibal's briliance, and Fabius' cunning... he resigned as co-Dictator.
Frustrated that Hannibal had now roamed the Italian countryside with impunity for years, the Senate recalled Fabius (at the end of his term) and elected two Consuls, Varro and Paullus. The Senate sent out both Consuls with their legions in a single army. Law required the Consuls to alternate command daily. According to history (Polybius), Paullus was patient and disciplined while Varro was rash and headstrong. On his day to command, Varro would double march the army towards Hannibal and the next day Paullus would proceed cautiously, if at all... and Hannibal learned all of this in due time. At Cannae, Hannibal set a trap for Varro. His double envelopment was the model and inspiration for the German strategy on the Western Front in WWI and WW2. Again, Hannibal inflicted an almost impossible amount of casualties upon the Romans... more than 30,000 men... 80-90% of the army!
By the way, Paullus was killed... and Municius... and a number of former Consuls, most of their military tribunes, and at least 80 Senators (the Senate numbered less than 300 before the battle). All those men whom Fabius had trained.... Stalin could not have purged the army as thoroughly.
In comparison, during 2003-2011, the U.S. suffered around 19% casualties... 16% wounded, 3% dead. Roughly 37,000. That's over an eight year period... The Romans lost over 30,000 men each at Trebia, Lake Trasimene and Cannae.
The Senate (who had suffered around 30% casualties at Cannae) begged Fabius to lead them. They followed his strategy to the letter. It took another twelve years to get Hannibal out of Italia, but Rome did it while also conquering Iberia and invading Carthage.
Fabius was not a brilliant tactician. Hannibal was.
Fabius preserved the army through the storm. Hannibal was the storm.
Fabius kept up the Roman morale. Hannibal grew more frustrated.
Fabius pulled his nation back from the brink of hell. Hannibal led his family, his nation, and his race into it.
