This is totally weird- a test to see if you're using your left brain or your right brain. I can see the lady twirl both ways, but it's easier for me to see her twirling clockwise (to get her to go counter clockwise, I have to look to the side and read something, and then she switches around). Supposedly only 14% of the people can see her twirl both ways, though that assertion isn't backed up by any research or other facts. The whole thing may be some sort of hoax, but it's interesting.
Give it a whirl.