From the /r/mylittlepony faq (select entries), couldn't say it better myself.
Why do you watch it?
It's a genuinely good show. It has great characters, all with different and likeable personalities, it has its funny and awesome moments making it entertaining and it gives a good lesson in the end that isn't shallow or boring, making it a fairly educational cartoon for anyone. All the people responsible for making it have a history of working on other great shows, here is an image showing it.
What's the appeal for adults?
Lauren Faust, the developer and executive producer of MLP:FiM, said that her intention with the cartoon was for it to be entertaining for little kids and their parents, so they could watch and have a nice time together. There are a lot of things hinted in the show that only adults normally get, like jokes with alcoholic drinks. And as said previously, it's a good show, despite the age it is aimed at, every person can enjoy it.
Okay, but why do male adults watch it? It's still a girl's cartoon, right?
So what if it is? Just because something is for girls that makes it bad for male people to enjoy it? That's an old and still common stereotype that something girly is considered bad just for being like that. It doesn't matter if it is girly, pink, has ponies, what matters is that it truly is a good show for every person, every human being. Gender is irrelevant.
Why does the internet love it so much?
It all started back in 4chan, but making a long story short, fans felt like standing up against all the hate and spread the message of the show since it's really good despite what your first impressions may be. There are also references thrown in the show all the time, and you know how the internet loves those kind of things. To show you an example, they've made a reference to the movie "The Big Lebowski" on a cartoon that is "for little girls." There is a character that has lazy eyes because the internet loved it and the makers, who made it that way in the first place as a mistake, decided to keep it that way.
What's so great about the community?
It's hard to see deliberate hate in it, it's filled with people that try to be nice and respect each other more than what we normally see on the internet, be it if you have a different opinion than they or if they disagree with you on something, those are not a reason for the community to hate you just for that. Plus, there are so many great artists releasing amazing art, videos, stories inspired by the show every day, it's a community full of good content.
