Alexander the Great had several traits that can be argued to make him great.

I have a pet theory where I use four criteria to determine a General and his skill.

Organisation.

Can the general organise troops so they fight welland the civil society to provide him with more troops, supplies and other things needed to fight. Can he keep himself involved only at a level above and a level below his own, to have focus on what he needs to do? Does he understand logistics?

While Alexander inherited a very well-organised army from his father, Phillip, he also showed that he could handle logistics (naval supply of his army while marching across the Sinai into Egypt is a good example of this) and capable of integrating new allied forces as well as adapt his tactics to new threats (such as Indian war elephants). I would rate Alexander as very good here.

Tactics.

Can the general win battles under different circumstances, against differing and sometimes superior opponents? Can the general delay superior opponents and keep his forces together under dire circumstances? Can the general handle a guerilla insurgency as well as a line battle?

Alexander proved that he could handle field battles, small skirmishes, large decisive battles and have his forced adapt to the field of battle - the denying of his flank at Gaugamela was an excellent tactical move. I would rate him as superb here.

Strategy.

Can the general see the big picture, can he use his victories to knock out enemies of the war, can he follow up on successes and not go headlong into pursuits where he will be stranded? Can he get allies and improve his positions without fighting? Does he have an understanding on how to undermine the enemy ability to fight?

Here Alexander shines as well. He understood the need to neutralise the Persian navy to secure his communications and access to reinforcements before chasing after Darius - thus the siege of Tyre and later of Gaza. I would rate him good to very good here.

Politics.

Can the general keep in position despite others trying to remove him? Can he get allies, can he work with those allies? Can he secure resources from himself, work with his seniors, juniors and equals? Can he drum warring tribes together against a common foe? Can he build a legacy that lasts? Can he appoint the right men to the right place and promote competent people?

Here you can argue back and forth. Alexander was very good at maintaining his public image, securing him the support of the Greek city states (coerced or voluntary) as their liberator and defender against the Persians. He managed to secure resources and reinforcements and quickly integrated conquered people and their elites in his empire, making them willing servants rather than chafing slaves or subjects - this angered his macedonian troops and his generals, but not enough for any of them to actually revolt, which is a very important balance to keep in this era.

The only failure is for him to build institutions that would survive him after his death. His empire fell apart, but the daidochi, his successors would rule most of it for 200 more years.

Generals that have skills in all four areas can be called great - even if they are inferior in some areas to other generals. I would add men like de Gaulle, Octavian, Phillip of Macedon, Frederick the Great of Prussia, Gustavus Adolphus of Sweden and Suleiman the law-giver of the Ottoman Empire to the list of great generals.

Here I make a similar rating of Hitler's ability and over here I rate a series of generals in case you want to read more about this pet theory of rating generals.

I know he was an exceptional general, at least that's what I've heard. But what exactly made him so exceptional? Or is it mostly just hype?

Well for starters Alexander is famous for being among the first to use combined arms tactics during battle. Combined Arms back then meant heavy Spearman infantry supported by cavalry on the sides to prevent the Macedonians from getting flanked. This potent and efficient combination of forces was very advanced for its time:We are talking ~300 BCE here.

Something to note as well is that Alexander often personally led his troops into key parts of battles. At the Battle of Guagamela, Alexander charged directly at the enemy leader, Darius III, causing him to flee and leave the Persian army leaderless.

Other things Alexander dabbled in during his long journey from Macedonia to India: siege warfare, river - crossing warfare, anti-guerilla warfare, and more. All at the age of ~22.

If you are interested in more detail you can read about it here: https://www.google.com/url?sa=t&source=web&rct=j&url=http://www.dtic.mil/dtic/tr/fulltext/u2/a350056.pdf&ved=0CB8QFjABahUKEwj_pbPkktjIAhVDHT4KHbKxBEo&usg=AFQjCNEz8u-ickh7kM4mP1cnyR80M6WB-g

Source: Study of Combined Arms Warfare by Alexander the Great , by Major Robert Pederson