bro-ny, noun: An adult fan of the show My Little Pony: Friendship is Magic, usually male but can refer to female.
People on 4chan noticed, thanks to the hyperbole of an article on Cartoon Brew, that the new My Little Pony show was actually quite good. Then when later episodes came out, they found that it was really good. This sparked a huge outlier fandom that call themselves bronies, which as of this writing (August 2012) is one of the most vocal, obsessive, and productive on the internet.
Productive. As in, there is fanfiction (check fimfiction.net), fan-made comics (especially on DeviantArt), fan-made Tumblr blogs (such as the popular Ask Surprise, Ask Hotblooded Pinkie Pie and Slice of Life), fan-made creative redubs of the show like Friendship is Witchcraft, fan-made Flash animation, fan-made music both remixes of the show's music and original pieces, and fan-made video games, like the highly anticipated Fighting Is Magic, which has gained attention from outside of brony circles.
I'm on the edges of the fandom myself. I like the show and read comics and the odd interesting fanfic, but I don't have a pony-related handle, and find once in a while the odd image that's a little too sappy (an unfortunate tendency of pony fan-art). The best ones, however, hit that sweet spot of show-related awesome and internet irreverence that make the best memes so dang catchy.
Some things to keep in mind about Bronies:
1. They are not furries.
One might argue that this is just quibbling over terms, but the brony community seems to get other things from the show than the furries get from their cartoons that make a distinction useful. Particularly, and this of course is a matter of opinion, fans tend to be less "creepy" about their obsession. Most bronies don't want to have sex with cartoon characters, or dress up as ponies except in an ironic manner. They do tend to hold onto the ideals of the show however, which is particularly important because the show, aimed as it is towards young children, is extremely non-sexual.
2. However, they can be just as adult, and profane, as any other internet subculture.
And how. Although the show is innocent the fanbase is not, and it's not uncommon for fans to use profanity and sexual references in memes. The culture did originate on 4chan after all. In fact, this juxtaposition of the innocent and the profane is a major source of brony humor.
3. They are heavily trolled.
This is perhaps another aspect that began from their early history on 4chan. Even taking that into account, there are surprisingly many people who seem offended that grown men could like a show about pastel-colored horses. Add in the media's perpetual attempts to find ratings-boosting supposed deviants to expose and/or weirdies to mock. Fox News and the Howard Stern Show, in particular, have shown themselves to be enemies of the brony subculture.
4. Despite the trolling, bronies tend to be non-confrontational about it.
They take a prominent message of the show to heart: to turn the other cheek and make friends with those who would disparage you. There is a prominent image macro of a determined Twilight saying "I'm gonna love and tolerate the SHIT out of you" that accurately sums up the fans' opinion of trolls.
5. Despite obsessions, most of them have a pretty good sense of themselves.
You might consider this to be a surprising characteristic, although really most fanbases have it if you dig down into them. You can find exceptions (and media organizations who take the "news of the weird" or "look at the perverts" angles to the fandom delight in finding them and shoving microphones in their faces), but the great majority of bronies know, to quote Mystery Science Theater 3000, that "it's just a show, and they really should just relax." PONY is not a holy thing with them. This is obvious to anyone spending time inside the fandom just from the amount of profanity and character remixes there are (such as Princess Molestia, MLP's very own Pedobear). They like it a lot, and unironically, but they are generally self-effacing about their own reaction to it. I think it is this aspect, more than anything else, that proves the innate healthiness of the brony community -- they really are just a bunch of grown people who greatly like a kids' show, who know how silly that is and can playfully mock the phenomenon even while being a part of it.