Exposure is the amount of light allowed to hit the sensor. With too little, the photo is grainy and dark. Too much exposure will result in clipped highlights, with washed out skin tones or skies. Either way you lose important detail that should be in the photo. Usually, cameras are pretty good at picking exposures automatically, but if you try to do anything fancy, like low key, high key, or high-contrast photography, your camera's automatic settings are easily confused.
If you're still just learning the ropes, you could try one of the scene modes. Most cameras have scene modes for indoor photos, bright sun, cloud cover, and night time portraits, at least. Pick the mode that best fits the circumstances and shoot. Most of the time, none of the scene modes are able to do what I want. If you want even more control, you should be looking at priority modes, or fully manual exposure controls.
The Exposure Triangle
Before you learn about exposure priority modes, it's important to understand the settings that control exposure. There are three of them, and changing any one of them will change what the other two need to be set at to produce a proper exposure. They are:
Aperture - Also called f number or f stop. The aperture is the size of the lens opening. Aperture is expressed as a ratio with focal length of the lens. That is, if the focal length is 8x the diameter of the aperture, f number is f/8. Because the f number is expressed as a fraction, bigger numbers represent smaller openings, and let in less light. If you double the f number, you cut the diameter of the aperture in half, and increase the required shutter duration by four.
Shutter Speed - Shutter speed is a measure of the time that the shutter remains open to let light into the camera. Shutter speeds are expressed as fractions of a second, so, like apertures, bigger numbers equal less light. The shutter speed 200 means 1/200th of a second.
ISO - ISO determines the sensor gain. Think of it as a volume knob for light. If you have the aperture and shutter speed set where you want them and there still isn't enough light, you can turn up the ISO setting to compensate for the shortage. A warning though—turning up the ISO comes with a side-effect: digital noise. Imagine you're listening to a radio station and the signal gets so weak that it starts getting lost in the background static. You can turn up the radio to compensate for the weak signal, but you'll also turn up the static. Recent advances in sensor technology suggest that, in the future, digital noise will not be the same worry that it is today, but for now, keep in mind that you want to keep the ISO as low as possible. If you can add light to the scene (open a window, etc.), widen the aperture or slow down the shutter speed instead, take those steps before you reach for the ISO control.