I started using it when I found that a lot of the blogs that I liked were from tumblr. There's a lot of image culture going on, with lots of blogs dedicating themselves to art or Sims glitches or really good animated gifs or awesome tits.
I think part of what makes tumblr different is the act of reblogging; making a successful tumblrblog isn't just about having lots of good OC, it can also be just collecting things from other sources and curating them to a particular kind of taste. These are really the ones that I enjoy most. Word of Command, waynedwaynetheterryhulkhoganrockjohnsongretzky, scary mansion aer some of my favorites.
It's kind of an in-between of twitter and blogging, where you have a simple way to share messagesthat are to the point (often just a short paragraph or picture will do) and people tend to create different sorts of interests or personalities for each individual one.