Bronies simply means people who are of an older age group and like to watch My Little Pony: Friendship is Magic. There is nothing particularly exciting about this, but they make a big deal out of it.
Jump on to a forum most places online, and you will see these people often pushing their fandom. As in, you will be on a forum for cars, and someone will have their display picture as a pony, and all their posts will be about ponies. Then when people accuse them of being off topic, they go into a rant about acceptance, as if watching a cartoon is some sort of big revelation.
Subculture is one thing, but it is a totally other thing to push it into people's faces and then get upset. It would be like heavy metal fan jumping on to a My Little Pony forum and spending their whole time talking about metal, and then getting upset that they aren't well received.
As such, bronies are known to complain about acceptance, and about how hard it is to live in a world like this. News flash fellahs, no one really gives a shit. People don't hate that you like My Little Pony, they hate that you won't fucking shut up about it.
Brony: Hey guys, I know this is a post about motorbikes, but did anyone watch My Little Pony yesterday? Wow!
Regular poster: Umm...that is a bit off topic, don't you think? What is with all these posts about ponies?
Brony: Us bronies just want to be treated like everyone else. Why do you hate us for our subculture?