I honestly don't know. I would suggest maybe it's a combination of
* Filter choice and options (maybe not the most varied, but limits are sometimes beneficial)
* User base (a huge driving force of the whole experience is people finding each other, liking, commenting, etc.)
* Social aspect and promotion (who wouldn't like having their image on the popular page and finding lots of random new followers when next logging in?)
* Integration with social networks - flickr, tumblr, twitter, etc.
* Focus on core features, not bloat - Do they even have a proper website yet?
* Timing
* Luck
I've tried many of the other apps available and for one reason or another, something has either put me off them or not kept me interested in the way instagram has.
Even if another application replicated and bettered every feature, they wouldn't necessarily be better - simply because they lack the users and culture that instagram have built up.