In case you haven't figured it out, the blog is named after the shapes that are used to kill groups that have only one eye.
As usual, the best reference is Sensei's Library.
In fact, I ripped these images from there:
The key here is almost fill. This means with one empty point still inside the eye, not two or more. This means that once the shape's outer liberties are filled, it will be forced to capture your killing shape. After it does this, it's your turn, and you can play on the vital point shown in the pictures.
In practice, the sequence of events is not played through, because both players can see this coming.
Additionally, there are other circumstances -- for instance, a bent four in the corner is also a killing shape, but only in the corner (I lost a game at tournament today because of this!)
So, know your killing shapes.