1. The world - I feel like people overlook this one a lot. The world of Equestria is broad and fascinating. It doesn't always make total sense and it's rarely the focus of the show, but it's very consistent for a children's cartoon with over 180 episodes and a movie. In my opinion it's a pretty unique combination of fantasy/mythological and modern elements.
2. The characters - The mane 6 and supporting cast are all interesting characters. They're complex, they don't always get along, they live different and consistent lives and they fit their world perfectly. Sure, Lauren Faust and Hasbro didn't exactly invent totally novel characters, but they did make round and dynamic characters who were archetypes more than stereotypes and grew as the story progressed. The voice actors are all top notch as well.
3. The production value (i.e. everything else) - The animation is strong, if pretty simple in the earlier seasons. The sound effects and background music are great and well made. Daniel Ingram is a maestro who has produced dozens of songs for the show that range from good to stellar. Plus, the staff at DHX and Hasbro are great at putting little touches into the show that make it feel more real and engaging.
For sure its IP's popularity helped it succeed and the unexpected brony fans didn't hurt, but even without those two things, say, if the show didn't have the MLP logo and never really picked up a large adult following for whatever reason, I'm pretty certain it still would have been a very successful show.
Oh, and Lauren Faust is some sort of magical fairy who spreads super success pixie dust over whatever she touches, that helps too.