Bokeh is the name of the shape that can be seen in photos or movies when objects are out of focus. Bokeh DoF is a method where a textured quad is rendered for each pixel using a texture to define the shape to reproduce the effect produced by camera lenses, which gives a filmic look to the scene.
The actual implementation does this performance intensive effect only in half resolution. It also tries to save render performance in areas where this is not that noticeable. See Adaptive DOF for more information.
The Bokeh method is far more costly performance-wise, making cinematics and showcases prime candidates for the Bokeh method as the appealing visuals often outweigh any performance concerns in those situations.