What is ambient occlusion? Ambient occlusion "is a shading and rendering technique used to calculate how exposed each point in a scene is to ambient lighting.

Ambient lighting is regarding to What is ambient lighting?:


  ... lighting to be constant and independent from position: that's ambient
  lighting.


If ambient lighting has no fixed position, how can points then be more or less exposed to it? Ambient lighting is "shining by a constant amount in all directions." So if the light is coming from all directions, every point should be exposed by the same factor to the ambient lighting.
Your point is correct when applied to ambient lighting as an approximation technique. This crude approach does indeed give the same lighting level to all surfaces regardless of their surroundings.

However, ambient occlusion is a different (less crude) approach, that models how the light levels in a real scene vary depending on how much reflected light can reach a surface. The confusion is due to two very different approaches having similar names.

Ambient occlusion is a much better approximation of what in real life is described as ambient light - light that arrives from the background rather than directly from a light source.


  If ambient lighting has no fixed position, how can points then be more or less exposed to it?


When used in the context of ambient occlusion, the term "ambient lighting" still means background light approximated as being the same in all directions, but the surface is lit based on how many of those directions are not occluded by objects in the scene.

This gives subtly varying light levels that give much more realistic images than with a single level of ambient lighting. This gives the effects seen in real life such as the corners of a room being slightly darker than elsewhere.