Exposure as it applies to photography simply means how much light made its way through your camera to the imaging surface.  Given the ISO setting of that surface did enough light make it to the sensor to define the image?

Well, if one photon made it through then you have an exposure.  Its a bad exposure, meaning it will be rather dark, but sure, its an exposure.  The goal, artistic considerations aside for the moment, is to have no, or at least very very few areas of either pure white (over exposed) or pure black (underexposed).  Once you hit pure white or block no amount of post processing can recover any detail from those areas.

On many digital cameras you have a display you can turn on called a histogram.  Honestly, I would consider the histogram one of the requirements for any camera you buy.  The histogram tells you at a glance whether you got your shot or not.  There are only 2 parts of the histogram you need to really understand, the far left and right edges.  The left edge is black, the right edge represents the whites.  The histogram itself is a counter of how many pixels in the image are of a given value.  Once you get it you will wonder why it is so complicated, but let me try to explain, because it is sometimes difficult to comprehend at first.

On the histogram you have a graph.  It looks like any other graph.  Some will be a single black/white graph, some will have all three colors broken out.  But in the end, they are all the same.  You want the lumps in the graph to be anywhere except the left and right edges.  One or 2 pixels into the graph, no problem.  But if you have a big bar on either end right up against the edge, that means you have a region of pure black or pure white.  Even if you are shooting pics of a bride in a white gown you really dont want that white edge being so prominent.  Slightly grey, or underexposed, will produce a much more detailed image that will reveal the texture of the dress, or maybe the beadwork, or other details.

More to follow, this is not a completed article.