This is going to be long, rambling, and unsourced, so take it with a gain of salt, but here's the gist of it:

Zoe Quin is a female indie game maker who focuses on experimental games that explore very non mainstream topics. The game that seemed to thrust her into the spot light is a browser game about depression. It got favourable reviews, which seemed to have seriously annoyed the part of the internet that thinks death threats are a valid way of expressing dissent.

Then her ex posted a rambling essay that accused her of having a relationship with one of the game journalists that gave her a good review. This was proven to be false, but gave the trolls that hated her a convenient rallying cry "ethics in game journalism."

Others became targets and polarizing figures joined, probably making it worse, unintendedly. It rapidly grew to become extremely misogynistic and escalated to scum from all sides to treat it like a holy war and just generally make a mess of the gaming community.

I'm sure there are people in the gamergate side that really thought it was about ethics, but digging deeper it really seems to be misogynistic in nature and an attempt to silence nonstandard games, those that make them, and those that support it.