This post is for Jared and anyone else who needs help digesting my posts.

• Aperture – Size of opening for light to enter. It is controlled by a combination of physical limitations of the lens tube, as well as aperture blades which can tighten or open at the photographer’s command. Apertures are measured in an “f” number, which has an inverse relationship property. f/1.2 is very wide, whereas f/32 is nearly tiny. While most lenses are physically capable of almost all apertures larger than about f/8, if the optics are not designed for that aperture, then there is no capability of obtaining focus at that range. For that reason, lenses are designated with their largest aperture available in their name, for example, my 70-300mm lens is f/4.5 – f/5.6, meaning that it will have a lens aperture of at most 4.5 at its widest angle (70mm) and 5.6 at its most zoomed angle (300mm). Lenses below f/3.5 or so are usually called “fast” lenses, because they take in more light than lenses with a smaller maximum aperture, making them capable of capturing faster motion and taking much sharper images. At the other end, we have settings like f/32, which is like a pinhole of light, this gives a much deeper depth of field than the smaller numbers ever could, and can also be especially useful in intentional blurs (even in daylight).
• Focal Length – Length of the tube, kind of. It is a representation of the distance between the front optics and the rear optics after allowing light to bounce around in the tube or something. The technical definition of it is not particularly important, but if you care, see the Wiki article. It is important to note the standardized version of the focal length. Standardized focal lengths are converted from their physical length by multiplying by the camera sensor crop factor, for most DSLR users, that number is 1.5 (Nikon) or 1.6 (Canon). Focal length in general (once standardized) indicates how much you can “zoom” or how wide you can shoot. Below 50mm, it is wide, above 50mm is zoom.
• Filter Size – Does not affect optics, just a number that says how big the screw is on the front of the lens so you can mount filters or other fun things on it.
• Elements/Groups – The number of elements is the number of physical pieces of glass that exist in the lens and groups is the number that move together. In general, a more complex optic set will result in a better quality image. 
• VR/IS – Vibration reduction (Nikon) and Image Stabilization (Canon, Fuji) is a function that will reduce blur due to camera (or operator) shake. It is also useful for taking pictures from moving vehicles or otherwise in a situation where the camera is hand held, not on a tripod. The optics adapt when this function is turned on, it attempts to keep the image centered. In Normal mode, this shake is only up and down, allowing for panned blur. In Active, the image is stabilized in all directions
• A/M, Auto, M/Manual – Focus modes. Some lenses are manual focus, the photographer must adjust focus him/herself. Some lenses are auto focus, and there is no intervening in the process. More common though, lenses are Manual and Auto switched. You can usually change between manual and auto by a switch right on the lens body. Another mode is A/M, which is an autofocus mode that also allows for photographer adjustment of the focus, in case the auto focus gets it wrong.