simplistically, exposure is how light or dark your photo will be, if it is too dark for your liking then it is under-exposed, conversely, if it is too light, it can be said to be over-exposed.
exposure is important in cameras because cameras cannot record detail dark regions as well as the brightest regions in the same way that our eyes can.
in other words, the camera as a recording device has a limit in its dynamic range of light values it can record in the one photo and if you try using Photoshop to lighten or darken the photo, you will find that either the darkest region when made lighter will just produce image noise and not much if any detail, or if you try to darken a photo, the lightest areas tend to stay light or became a strange colour but you do not get much if any detail in these areas that have been “blown out” by over-exposure.
so what we usually aim to do is set the exposure so that the most important part of the scene (eg. skin) is displayed well and as similar as possible to our usual visual experience.
camera manufacturers provide automatic exposure settings on cameras which are designed to adjust the camera's various parameters which modify exposure to produce a result that most of the time is acceptable in terms of exposure. This setting is usually marked “AUTO” or “PROGRAM” on the exposure mode dial. The camera has light sensors which measure the incoming light and then adjusts aperture and shutter speed, and in some cases the ISO (camera sensitivity to light).
of course, sometimes we don't want the scene or skin to be as we see it but darker or lighter, and we may need to over-ride this by either setting the exposure manually or adjusting the “exposure compensation” setting - this is particularly the case when using a flash as we often prefer to soften the effect of the flash by reducing its exposure in which case we may need to either use a manual flash mode or adjust the “flash exposure compensation” setting.
these compensation settings are measure in terms of EV (exposure values or “stops”)
1 EV or 1 stop difference represents a difference of half (if minus 1EV) or double (if plus 1 EV) the exposure.
exposure can be doubled by either:
doubling the duration the shutter stays open - eg. 1/125th sec instead of 1/250th sec
doubling the ISO (sensitivity of the camera or film) - eg. ISO 200 instead of ISO 100
increasing the diameter of the lens aperture by 1 f-stop or stop
aperture is measured in f stops and for the beginner, this is perhaps the most confusing aspect of exposure.
apertures with differences of 1 stop between them are f/1.4, f/2.0, f/2.8, f/4.0, f/5.6, f/8, f/11, f/16
thus you can double the exposure by using f/2.8 instead of f/4.0
the f ratio number actually comes from the focal length of the lens divided by the lens diameter
the camera can close the aperture down at the time of the exposure to a designated f stop setting
when the term “stop down the aperture” is used, it means use a smaller aperture (ie. a larger f number).