Overexposure and underexposure when used correctly can give nice and unusual effects when used intentionally but when you first venture out of AUTO mode into Manual or AV mode it can get annoying when the shots you take are too dark or too bright so let's have a look and see how this whole exposure thing works.
Okay, so this is what my camera thinks the correct exposure is. Dark room, light source is just a standard bedroom light bulb.
Canon 85mm F1.2 ii USM L, ISO 800, F1.2, 1/250th
Canon 85mm F1.2 ii USM L,  ISO 800,  F1.2,  1/250th
Canon EOS-1D Mark III @ 85mm, F1.2, ISO: 800, 1/250th
1/250th second shutter speed which is just fine for handheld shots of static objects at 85mm. If you're wanting to shoot something that moves faster then up your ISO until you're getting about 1/640th or to be extra safe, 1/800th second shutter speeds. I used a paper bag with a white inside as an example so you can see how different exposures affect the lightest and darkest colours at the same time. The camera has done a good job. The exposure is more or less identical to what I see with my eyes.
Canon 85mm F1.2 ii USM L, ISO 800, F1.2, 1/640th
Canon 85mm F1.2 ii USM L,  ISO 800,  F1.2,  1/640th
Canon EOS-1D Mark III @ 85mm, F1.2, ISO: 800, 1/640th
Now this is the same image slightly under exposed. I moved the black mark for exposure to the left a few stops so it's now at -1 1/3. The detail in the black outside of the bag is now mostly lost but you can still work out the shape of the object. Also a slight underexposure like this can be fixed using photoshop or other photo editing software so if your image is slightly underexposed, don't panic - this image could easily have it's exposure fixed with a little editing. By underexposing a little I've also gained a much faster shutter speed. It's increased from 1/250th to 1/640th.
Canon 85mm F1.2 ii USM L, ISO 800, F1.2, 1/1600th
Canon 85mm F1.2 ii USM L,  ISO 800,  F1.2,  1/1600th
Canon EOS-1D Mark III @ 85mm, F1.2, ISO: 800, 1/1600th
This image is heavily underexposed. The black mark is now far to the left and set to -2 2/3. The image is mostly lost in darkness and yes it could be fixed with editing but at the risk of lots of image noise due to the camera's eye not being open long enough to take in the information it needed and at 1/1600th it's not surprising, that's a long way away from the camera's suggested exposure of 1/250th ! If you've seen images like this often, keep an eye on your exposure mark and you'll find it's wandered too far to the left - either that or you're in a very dark environment !!
Canon 85mm F1.2 ii USM L, ISO 800, F1.2, 1/160th
Canon 85mm F1.2 ii USM L,  ISO 800,  F1.2,  1/160th
Canon EOS-1D Mark III @ 85mm, F1.2, ISO: 800, 1/160th
Now let's go to the other end of the scale "Overexposure" where the camera eye is left open longer than usual which lets more light into it, giving you brighter pictures. Here the marker has been moved to the right just a little to make it +2/3 over what the camera thinks the correct exposure is reducing the shutter speed from 1/250th to 1/160th. Overall it doesn't look too bad. There are more highlight details in the surface of the bag than at the "correct" exposure and the whites on the inside of the bag are not overexposed enough to blow out. The only real problem is the drop in shutter speed to 1/160th - unless you have very steady hands you'd need to increase the ISO to prevent the possibility of image blur.
Canon 85mm F1.2 ii USM L, ISO 800, F1.2, 1/100th
Canon 85mm F1.2 ii USM L,  ISO 800,  F1.2,  1/100th
Canon EOS-1D Mark III @ 85mm, F1.2, ISO: 800, 1/100th
Cranking the overexposure dial further to the right to +1 2/3 as you'll now expect, the shutter speed slows due to the extra time needed to let more light into the lens and has now dropped further down to 1/100th meaning ISO increase is needed ( or a tripod ) for static objects. At 1/100th tripod mounted will still give a blurred image on anything that is moving so in these instances, ISO should be increased even more. The image itself still doesn't look too bad. There is much more detail in the black part of the paper bag and the white still hasn't blown out so in situations where you want to bring out details in darker objects, overexposure is a useful thing.
Canon 85mm F1.2 ii USM L, ISO 800, F1.2, 1/30th
Canon 85mm F1.2 ii USM L,  ISO 800,  F1.2,  1/30th
Canon EOS-1D Mark III @ 85mm, F1.2, ISO: 800, 1/30th
And here to the far right of the exposure mark at +3 you can see the brightness is starting to make the image look washed out. The shutter speed is now at 1/30th which means you're going to want to increase the ISO substantially to get the 1/250th shutter speed back. Due to this originally being the colour black in a dark room, even at +3 exposure, the image still hasn't blown out but when shooting in daylight and shooting anything you can pretty much expect nothing but blown out and unusable shots which you'd have trouble saving even with editing. In manual mode you could increase the overexposure even more but unless you specifically wanted whited out, blown out images you'd have no need to.
So to wrap things up, if you're taking portraits of people in AV mode and they are blown out ( too much light ) then you need to move the exposure mark a little to the left to underexpose a little. And vice versa if you're finding your images are coming out too dark then move your exposure mark a little to the right until you get the levels you're after. More light = slower shutter speed, less light = faster shutter speed.
Also.. if you're shooting a model with darker hair then over-expose a little to bring out the details in it and with a light haired model, under expose a little to stop the hair from blowing out.