Quora discussion from 2010: "What makes Instagram cool?"
Mark Hendrickson had some interesting things to say (edited for length):
It taps partly into our desire to feel creative, but I think that more importantly it taps into our desire to appear creative to others. Snapping a photo with Instagram and applying a filter suddenly makes that photo seem inspired, even though the original subject matter was probably rather boring and the original shot poorly taken... It also provides others with a lens into your life that makes that life look cooler than it probably was at the moment. Others might get a little jealous that they weren't there to join you for it.
This is all to say that Instagram successfully feeds our Hipsteresque vanity.
Adam's answer was also good (though not as fun to read as Mark's snide commentary!).
If you're not logged in to Quora and having trouble reading Adam's answer, try the permalink. Perhaps the most interesting takeaway from Adam's answer is that he's asking for better Facebook integration: "My one (missing) feature request is that it stick my photos in a Facebook album the way it does for me in Flickr and Instagram itself."
I'm guessing Lord Zuckerbeast will soon grant Adam's wish!
Actually, Instagram released this feature in 2011. Done!
Anytime you're on Facebook and see a folder called Instagram Photos, that's it.
Other good reads from Quora about Instagram:
History of Instagram by the founders
Why Instagram is worth a billion dollars by Scoble