It was considered one of the most important battles in military history mostly because of the extensive use of cannons and gunpowder to bring down the massive walls of the city, which were considered impregnable. After that siege extensive defensive fortifications became a lot less important and had to be adapted to the new reality of gunpowder warfare. In fact from then onwards fortifications became less and less relevant to the point they eventually disappeared. The fall of Constantinople essentially marked the coming of a new age in warfare.

Furthermore it was also important because it marked the definitive end of the Roman Empire but also because it completely changed the geopolitical realities of the entirety of western Eurasia. The Byzantines had effectively isolated the rest of Europe from invasion from the east for centuries while at the same time allowing for extensive trade with the wealthy eastern mediterranean and beyond, once they were gone they left a power vacuum wich allowed for the turks to penetrate further into Europe and even threaten Vienna for a time, the unstable situation in the east med. and the religious tensions between christianity and islam ( which now was in control of the entire southestern europe and middle east) also contributed to the interruption of trade with the east which eventually led to the rise of the maritime colonial empires of western Europe wich strived to find a new way to the Asian markets through the sea.

why is it considered to be among one of the greatest battles of all time, up there with the Battle of Waterloo, Invasion of Normandy, etc.?

Is it? First I've heard. Who's saying this?

Sometimes It's very important to distinguish between importance and impressiveness, especially when it comes to battles. The fall of Constantinople was not a particularly impressive battle for either side. But, the fall of Constantinople had some very important socio-political ramifications.

1. Despite the split between Catholic and Orthodox, the Byzantines had long been seen as the bulwark of Christendom against the Islamic/Eastern tide. After all, the only time the city had been truly sacked was during the Fourth Crusade. This image outlasted the reality, so when the city fell it made the Ottoman advance seem that much more terrifying. It made it seem as though all of Christendom was at risk of invasion, including Rome. Mehmed II helped this idea along by actually invading Italy and sacking at least one city (Otranto). The fall had effects as far away as Spain, where the Muslim state of Andalusia went from a uneasy neighbor to a potential Ottoman beachhead.
2. The Ottoman stranglehold on commerce to the east was strengthened. This has already been covered.
3. The fall had an interesting effect upon Russia, which was now the leading Orthodox area. Or at least the largest. This effect has become known as the theory of the Third Rome. It basically goes that the Russians now saw Russia as the true (and final) home of Christendom. Moscow was to be the "third Rome" or home of Christendom now that Rome and Constantinople had at some point been invaded. Also, Russia's access to mainstream European thought was severely cut off by the city's fall. Much of the fervor of the Russian Orthodox Church can be seen as a result of this. Some. Not all.

Sources ( Sorry for lack of authors. I'm at work at the moment. Don't tell) "1453" "Isabella: Warrior Queen" "The Icon and the Axe"