Circles of Confusion

One of the things in an image that a circle of confusion (CoC) is responsible for is bokeh. CoC are a bunch of circles that overlap each other and cover the whole frame, or sensor, and as the aperture closes, the smaller each circle becomes and the more out-of-focus areas appear to be in-focus. In fact, there really is no area that is "in-focus" as lenses do not perfectly focus all rays of light. It's just the areas where the circles of confusion are the smallest making the image sharp. The smallest circle that a lens can produce is called the circle of least confusion.

Because the circles are unlimited and overlap each other thereby forming the image, there is no way to take a photograph and show an example of a circle of confusion. A diagram is required.

the red line is the point of focus; the top and bottom diagrams show a lens producing a large circle of confusion on the sensor while the middle one shows a circle of least confusion because this distance is where the lens is focused

Depth of Field "in Depth"

When the circle of confusion is small enough, it is considered to be part of the depth of field (DOF). The Photography 101 article details DOF. See DOF Calculator.

As objects converge on the point of focus, their circle of confusion projected becomes smaller and smaller. What is acceptably sharp is subjective particularly as pixel counts become greater and greater in digital cameras.

"acceptable" depth of field is when the circles of confusion are small enough to be considered in focus

As the aperture closes, the angle of the light narrows and the circles of confusion become smaller thereby increasing the depth of field.

the narrower angle that the light is hitting the sensor makes for greater depth of field