Well, that’s really two questions. One is “what’s up with the ‘skepchick’ thing”, the other is “what the hell was the ‘elevator incident’ all about.”
The “skepchick” community is basically another iteration of the classic “we need a movement within X community specifically dedicated to women.” In practice, it’s largely served as a platform for the introduction of feminism, gender-based advocacy and a bunch of other stuff that has nothing to do with skepticism into the skeptic community. Overall, it’s caused a strong split within the community between people who are basically going along with it and people who are applying the basic tenets of skepticism to the issues raised and watching them fall apart. Most SJW statistics do not fare well in a room of critical skeptics, and this hasn’t been much of an exception.
Watson is overall better known for the “elevator incident”. In short, during the World Atheist Conference (2011) in Dublin, Ireland, Watson decided she was tired of drinking and wanted to head up to her room. She got into an elevator. Another person (a man) entered the elevator with her, and politely asked if she would be interested in talking over coffee in his room. It’s not 100% clear whether this was a simple invitation to chat or if there were further implications, but what is 100% clear is that Watson declined, and the other person made no further comment. That is, he politely asked her for coffee, she said “no”, and he proceeded to respect her declination.
Watson’s reaction to the incident was proportionate in roughly the same way a Tomahawk cruise missile is a proportionate response to a fly on your window. To wit, she proceeded to say a bunch of nasty things about the guy for doing precisely what most feminists have been claiming they want men to do: politely display interest verbally rather than physically, and politely and respectfully accept a “no” when given.
Then the atheistsphere slightly exploded. Lots (and lots, and lots) of people called her an idiot, highlighting her disproportionate reaction. In fact, Dawkins himself, an a moment of vitriol, basically shredded her. Shit hit fan. In the end, the overall incident and accompanying backlash was a huge portion of what has created the current divide within the skeptic movement between feminists and skeptics. (I would personally submit that mainstream feminism is inherently incompatible with true skepticism. You can’t be skeptical and still peddle the level of bullshit statistics that we see there, you just can’t.) Regardless, at least for the moment, the issue has created a major schism between those in the skeptic community dedicated purely to skepticism, and those who believe the skeptic community should be folded into the growing bubble of “social justice” advocacy.