1. Who is Zoe Quinn and how is she related?
The initiator of this whole scandal was Zoe Quinn (@TheQuinnspiracy on twitter), an indie game dev who made the nongame Depression Quest.
She is not what #Gamergate is about, she is however among the people responsible and as such it still related to the topic.
The thing Zoe did to spark this scandal was sleeping with 5 (or more) guys. The problem people have with this is not that she sleeps around, it is not that she had a boyfriend or that one of her affairs was married.
What really caused this outrage was that these guys are more or less influential in the games industry, especially Nathan Grayson (@Vahn16) being among the 5 guys is important here.
Nathan Grayson in case you don't know him is a Kotaku writer who happened to write a very positive article about Zoe Quinn just a day before they started their sexual relationship.
2. Faking harassment and causing depressed people to be harassed
One of the things she did to gain publicity was fake harassment from an image board known as wizardchan, you can find it here http://wizardchan.org/
One of the many problems with this is that wizardchan is normally browsed by people that actually suffer from depression.
I say actually because Zoe's game Depression Quest shows that she neither experienced depression herself nor researched the topic.
As a result to her making a huge drama about this she got people to harass these already depressed people.
3. Causing a game jam that supports women interested in game-making to shut down
She also led a similar hate mob up against a game jam group named The Fine Young Capitalists (@TFYCapitalists), she got their initial game jam taken down for being misogynistic.
What kind of game jam is TFYC that they get taken down for misogyny? They are a feminist charity fundraiser that wanted to make games for women that provide ideas.
Then Zoe made a game jam fundraiser called Rebel Jam on her own, this one however has no clearly stated goals, is complete nontransparent, without date or judges and the only payment method is a paypal linked to Zoe's private account.