There are many resources on the Internet and books that could perhaps explain Exposure in better detail than I ever could here. Consider this an overview and I encourage you to get someone else's explanation of this topic too, for your better understanding.
What is Exposure? Wikipedia says "In photography, exposure is the amount of light per unit area (the image plane illuminance times the exposure time) reaching a photographic film or electronic image sensor, as determined by shutter speed, lens aperture and scene luminance."
Huh? What? Let's look at it another way.
One photo is too bright, or over exposed and the snow has no texture. The other is too dark, or under exposed and the people - the subject - are indistinguishable from the background.
So Exposure is the amount of light that is captured by the sensor in the camera.
We can control this Exposure with three settings on the camera. ISO, Aperture and Shutter Speed. Lets see how they relate to each other.
ISO - or in the film days you may remember this as ASA - is a measure of the camera's sensor ability to absorb light. A low number (like 100) needs a lot of good daylight, and a high number (like 1600) lets the sensor "see" in dim indoor environments. Think of it sort of like a volume control.
Aperture is the relative size of the opening on the front of the lens. Wider open (like 2.8) lets in more light, while a small aperture (like 22) allows just a pinprick of light to get through. Think of it like a curtain that can be opened a bit, to let in just a bit of light, or a lot to let in as much light as possible.
Shutter Speed is the amount of time the sensor (or film - lets just assume we're working with digital cameras ok?) is allowed to absorb light. It is usually measured in fractions of a second. One-two-hundredth of a second is a good number. Think of it like opening and closing the curtains, so you get a glimpse of what's outside.
Where there are three, there is a triangle!
These three components of Exposure are interrelated. If you change any one, your Exposure will be brighter or darker.
For example, if you change ISO to a lower number (turn down the volume) the exposure will be darker.
If you change your Aperture to a smaller number (open the curtains wider) the exposure will be brighter.
If you change the Shutter Speed to a bigger number (open the curtains for a shorter time) the exposure will be darker.
We want to be in control of the Exposure so we can make the photo look the way we want it to look. It is our artistic intent, plus science and the physics of light.
We will explore each of these in a lot more detail another time, but for now appreciate the yin-yang of each of these. In any given situation, there are many equivalent exposures that will give the same amount of light, but each will yield a very different look. Which one is right? That's up to you.
Set your camera to A mode, also known as Auto mode or the green pumpkin.
Look through the viewfinder, and at the bottom of the screen are three numbers. ISO, Aperture and Shutter Speed. (To make them appear you might have to half-press (and release) the shutter button. Don't be alarmed if the flash pops up.)
Looking through the viewfinder, watching the numbers, point at different things around the room:
Point at the light. The ISO probably went smaller, as might the aperture.
Point at a darker area. What did the ISO go up to? How low did the speed go?
Point at a slighter lighter (but still darkish) area. What changes?
There is no specific photo to take in this challenge. Just look at the numbers and try see how they change in relation to the amount of available light and in relation to each other. What are the maximum and minimum values for each of the ISO, Aperture and Shutter Speed while you were pointing at different areas?