The exposure triangle includes the three things you need to keep in mind when trying to take a good picture; aperture, ISO, and shutter speed. All three of these work together to make a good picture. Sometimes when you adjust one thing you will have to adjust all three.
Aperture is used to adjust the depth of field. A low aperture of f/1.4 has a big opening, but a shallower depth of field. A high aperture of f/16 has a very small opening, but a wider depth of field. You would use a low aperture when taking pictures of birds or just one subject. And you use a high aperture when you are taking photographs of landscape. Aperture is measured F stops, and a low F stop has a bigger opening, and a high F stop has a smaller opening.
ISO is the measure of light sensitivity in your photos. If you have a low ISO of 100 your photo is less sensitive to light. If you have a high ISO of 3200 your photo is very sensitive to light. High ISO's result in noise on your picture. Noise is when the photo has a grainy look to it, just like the image above. If it is a sunny day outside and there is a lot of natural light, then you would use a low ISO of 100. If it was a dark day outside with not very much natural light you would have to use a higher ISO of 1600 or 3200 to let in more light.
Shutter speed is how long your shutter is open, and how long it lets light in. It is measured in seconds or fractions of a second. You would use a high shutter speed of 1/1000 to photograph a person running. You would use a slow shutter speed of 1/8 if you were photographing someone writing with light.
Understanding Exposure: The Exposure Triangle with Mark Wallace