It really was a scratch your own itch kind of thing. So many redditors complained about the crappy image sharing sites...lots of them were verboten to use on reddit because they were so spammy, or slow, or whatever. There was no clear leader in the image sharing space. Facebook was impossible (because it wants to own every user and won't let you show someone something without logging in), even if it were an acceptable place to upload weird random pictures (I know many people who do, but they just don't know about reddit and imgur yet). So...imgur's founder saw a very clear need, and humbly pointed redditors to it.
It took off because it was amazing in its simplicity and sincerity. imgur's founder clearly wanted you to share funny pictures in imgur, even if he couldn't figure out how to make it pay him money for every image. He just wanted to solve a very real problem that caused millions of people tiny amounts of pain. (When picking a problem, pick one that causes either a few people a lot of pain, or one that causes a lot of people a little bit of pain. You're unlikely to find a problem that causes a lot of people a lot of pain, since those are already usually very competitive.)