Okay so Stephanie Brown...what makes her so beloved and what do I need to know? :)

Sure thing, @jabberwocky1996!

Stephanie Brown is the daughter of the Cluemaster, who, for all intents and purposes is a C-List or D-List version of the Riddler. His criminal lifestyle meant that he and Stephanie had little meaningful interaction until he is supposedly reformed. However, he was in fact still a criminal, just cured of his compulsion to leave Clues at the scenes of his crimes, making him more dangerous. His daughter, angered that he’s still pulling jobs, uses her inside knowledge to become the vigilante Spoiler and repeatedly tip the cops off to what her father is doing. She then decides that she enjoys fighting crime and starts going after criminals other than her father.

She spent a nice while as a love interest for Tim Drake, aka the third Robin. During this time, she finds out that she is pregnant by an ex-boyfriend, gives birth, and gives the child up for adoption so that her daughter would have a chance at a better life.

Eventually, however, Tim follows the wishes of his father and briefly retires as Robin, and Steph convinces Batman to let her take up the role. Bruce never really trusted Stephanie the way he did the other Robins, though, and never even told her his real name. He eventually fires her due to her insubordination, presumably because he feels that it was that sort of behavior that led to Jason’s death.

This leads to a bunch of poor decisions on everyone’s part that I don’t even want to discuss. There’s falsehoods, there’s death, there’s false death, there’s upheaval, it’s a whole thing. Basically, though, Steph is believed dead for a few years before coming back and reclaiming her identity as Spoiler. 

This leads to other decisions that all strike me as questionable, including the deterioration of her relationship with Tim. She did briefly get an invisibility device, though.

She eventually becomes the fourth(?) Batgirl, and proves herself to Barbara Gordon, the second(?) Batgirl. She also finally learned Batman’s real identity. She kept the role for about two years before the New 52 erased her from history. However, she has been returned to continuity during the past year or so, though she’s essentially back to square one, with her time as Tim’s girlfriend, Robin, and Batgirl all erased. It’s not a great situation, but it’s not the worst case of the New 52 #@$%ing people over.

Stephanie is often characterized as one of the less naturally skilled of the Batfamily, a weakness that she makes up for by being both incredibly determined and having a talent for improvisation. She has proven herself capable of holding herself against members of the League of Assassins and even Superboy.

Despite her backstory, she usually comes across as one of the most well-adjusted and cheery members of the Batfamily, which leads to some fun interaction with Damian Wayne, who is arguably her polar opposite. She’s also kinda sassy and feisty. She’s good friends with the third(?) Batgirl, Cassandra Cain, with Cass helping train her and Steph helping to teach Cass to read. The New 52 has cast her as being roommates with Harper Row, aka Bluebird, a character who has been around for less time but who canonically is now more experienced. The New 52 also set her up as being on good terms with Catwoman, even after Selina became the leading crime figure in Gotham. Which, once again, is a thing in and of itself. She was also buddies with Supergirl prior to the New 52.

Overall, in a superhero family that is largely composed of brooding, self-destructive, hypertalented outcasts, Steph stands out as optimistic, light-hearted, vulnerable, healthy, under-appreciated, and a little more grounded. But she still has enough fire in her to fit in among this group. She is very relatable and has a lot of great interactions with other heroes. And I think that about covers it.