They stand out because they're so much brighter than the surrounding areas.
The out-of-focus blur is not gaussian; every out-of-focus point in the scene projects a fairly evenly-shaded disc, like what you're seeing, onto the sensor. These discs overlap and additively blend so that, in areas without much contrast, the result is a more-or-less smooth blur. But light sources can be much brighter than their surroundings, so the discs they project contribute almost all of the light hitting any given pixel in those areas, and thus stand out.
The reason the borders of the discs are often brighter than the centers has to do with spherical aberration. Lenses vary greatly in how they handle this optical distortion; it is closely related to how smooth and "creamy" bokeh they produce.