Emo is literally short for "emotional" - think unhappy goth who thinks the world wants them to Die Die Die. Unfortunately, most people use the term for just about any display of negative emotion, so it's gotten skewed.
Brony - a male fan of My Little Pony: Friendship is Magic. A portmanteau of "bro" and "pony". They think they're extra-special because they're fans of a kids' cartoon. Not all of them are bad, but most of them think they're seriously entitled to fandom bowing at their feet because they're MANLY MEN who watch a cute little children's show...
I'd put a slightly different spin on those:
Teens (and it's almost always teens) who consider themselves "emo" aren't necessarily depressed, but generally take that "teenage angst" thing to the extreme. It's a subculture which glorifies suicide and "cutting" (a self-harming activity some people do, either with or without the intention of actually committing suicide). In my experience there are just as many emo guys as there are girls and the fashions usually present in similar ways - lots of black, unusually colored/styled hair (often also black), black painted nails for both genders. Self-identifying as "emo" is a risk sign for depression and suicide, but isn't necessarily an indicator - some kids just enjoy finding an identity.
"Bronies" are guys (teens or adults) who are fans of the show "My Little Pony: Friendship is Magic," which is a re-make of the 1980's cartoons. It's actually a very good show and I'd recommend anyone who has Netflix to give it a try even if you don't have kids. I don't know where any of Liliane's "entitled" aspect comes from, honestly - several of my friends consider themselves bronies and it's mostly done in good fun. (There's a definite aspect of "I know I'm not the demographic for this show but I'm embracing it anyway and there's irony in that", but also they just like the show!)