Here's how the method works: the ambient occlusion coefficient at each surface point is computed by taking samples of the distance field at varying distances above the point long its normal. This essentially estimates the "openness" of the region above the point. Here is a more formal mathematical description:
Here is an output of just the ambient occlusion term.
Here is ambient occlusion with diffused lighting.
Also, I want to point out that, with ambient occlusion implemented, there is an unintentional "skyline" effect where the ground plane ends. This could be because the ray does not intersect anything and therefore the normal is undefined at those points. However, it does provide a nice gradient visual effect, where before there were curved bands going across as a result of numerical errors. Here's a better picture of the "skyline".