Well, as someone who has a great passion for animation, I've managed to pick up on some things I love about the show and what makes them so effective. I'm not an expert by any stretch of the imagination, but I do love animation in all forms and these are just some of the things I like about this particular series:
22 minute run-time.
The 22 minute run-time for the show is unprecedented in modern cartoons today. Most modern cartoons use the "squash-and-stretch" system of using 2x11 minute cartoon shorts in one episode to keep the numbers of its viewers up by not completely segmenting the show between advertisements, the reason for this is because they have the fear that some interest may be lost if the audience has to wait for the conclusion to an episode by having to wade through the ads just to see how things turn out. The downside of this is that there isn't much room for character development in these shorts, so the stories tend to be a little rushed and characters never really seem all-too well-rounded. The utilization of the entire 22 minutes is a bold move by Faust and it allows for the characters to develop and define their personalities, their own reactions to the conflicts and resolve it without resorting to ad hoc solutions while maintaining a genuine sense of flow within the three act structure. Adults (men especially) tend to enjoy this, as it gives them an incentive to remain invested and see how any drama or conflict is resolved since there is time for the plot to develop and the tension to mount as the stakes are raised.
The writing
Lauren Faust is a master of her craft, I can even admit to liking her earlier work The Power Puff Girls, as it is pretty much the same dynamic as MLP:FIM. The writing in MLP is of a very high standard, often switching things up by having sitcom style dialogue and actions often sitting beside, or mixing with the more serious non-pandering tones. The drama often feels fully realized because the characters each have their own methods of interpreting the consequences in their own way, even some of the sillier ones (like the pun-ridden "poison joke" incident) is a very real threat to the ponies and because after about two or three episodes you've come to know them at a quite personal level you do actually care about what happens. The show is also written to not bind itself specifically to any one age or gender group, nothing is dumbed-down or patronizing, everything has a distinct mythology or logic behind it which shows that the cast and crew have a lot of care for the show and want to get the best quality they can out of it. There are some very bold moves in this show that I don't see around a lot, like breaking the fourth wall, title dropping and cultural referencing (most of which are reminiscent of things that only adults would get, like the episode featuring the "diamond dogs" which is also an album by David Bowie by the same name).
Also, something else I love about it is that it doesn't try to teach you a message and instantly go back on it in the end. I've seen a few shows where hypocrisy renders the entire episode meaningless, it's always a disappointment.
The voice acting
Along with the decent dialogue and characterization, it would be nothing is the lines weren't delivered with much enthusiasm. Every character in this show has a very distinct voice and are easily recognizable even when they're not on screen. There is a lot of energy in whatever action or emotion is portrayed (even in Fluttershy), so the narrative is able to flow more easily as the ponies reactions to whatever is going on are communicated effectively enough for you to gauge the importance of the situation.
The animation
It's pretty fluid, easily recognizable and never cluttered or messy. I'm guessing this is achieved with either Flash or ToonBOOM Studio (or a combination of the two). The clear, bright colours, the design of the environments and other sets are simple and effective, you never feel like there's either too much going on or that there's an empty space that could be better utilized. To confirm this, just perform this basic experiment: take a random episode, or clip, and pause it at random intervals, study the image once it's a still and take some time to notice the composition, I'm yet to find a shot I don't like, and it's obvious that everything has been thought out beforehand in order to communicate the most effective message possible.
There are probably other things, but I've rambled on for far too long. If I've made any mistakes or you simply don't agree with me then please feel free to correct me.