I know that when I want to calculate Depth of Field by hand one of the variable elements in that equation is the Circle of Confusion. In layman's terms, what is the "Circle of Confusion," how do I calculate it, and is there any other ways that it applies to my photography aside from calculating DoF?
This is often a source of confusion which most people get backwards, so understanding this is delicate:
When a light entering a lens is not in focus, a point on the subject is focused into a circle on the image plane (sensor/film). This circle IS the circle of confusion. The more out of focus a point is, the larger the circle of confusion becomes. This depends on focus distance, subject distance and aperture. It does not depend on the capture device resolution or viewing conditions.
The circle of confusion used in DOF calculations is the maximum allowable circle of confusion which is considered in acceptable focus. This is dictated by the medium size and viewing distance because of the way human vision resolves details.
Historically, most DOF tables use a standard COC which corresponds to unaided viewing of an 8"x10" at 14" away for someone with 20/20 vision, although I am sure other magic numbers are used sometimes.
a lens is actually in focus at one point. as you move further from that point, the image blurs more. The amount of blur at a given distance from the focal point depends on focal length of the lens and the distance to the focal point.
The circle of confusion is the largest area blur that is indistinguishable from a point. It's dependent upon sensor resolution and film acuity. It also depends on viewing conditions and print size. The numbers you see used in calculations are just accepted standards.
It tends to be an easier concept for large format photogs as they deal with focal planes more.