Lets get technical, shall we?
The exposure triangle is basically three ways to control exposure that all connect with and and work together in different ways.
1. Shutter Speed
Shutter Speed controls how fast or slow your shutter opens and closes. The amount of time it is open determines how much time light has to enter your camera. Long shutter speeds create brighter images, while short shutter speeds create darker images.
But the light isn't the only thing that changes with your shutter speed. If your shutter speed is long, say at 1/15th of a second, moving your camera during the shot will cause a blurry image. For long shutter speeds, using a tripod is best.
Shorter shutter speeds, however, create sharper images with less movement and camera shake if you are taking the shot hand-held. A good rule of thumb is to keep the shutter above 1/60th while you are shooting hand-held.
Using a fast shutter may seem like the best option, as a long shutter will give you a blurry image in some occasions, but if you put your camera on a tripod, set a long exposure of, say, 30 seconds or a minute, place the camera on a beach with crashing waves, and click the shutter button, you can get amazing results with smooth, glassy water. Beaches aren't the only place you can do this, of course, any moving water will work. But who needs water? Put your camera in the middle of a busy street and see what a long exposure can give you. There are endless ways to play around with the shutter and get creative and interesting results.
2. Aperture
Aperture is the opening in your lens that lets light through. It can be big or small, and the bigger it is, the more light comes through. You can see how large your aperture is by looking at the F-stop on your camera. It often shows as something like this: F5.8. (with the number replaced with whatever your aperture is set at.)
But what use is a number to you if you don't know what it means? The bigger the number (F12, F16, F32), the smaller the opening. The smaller the number (F1.4, F1.8, F2.8), the larger the opening. (Yeah it seems backwards, I know)
So if you have a smaller number, more light will get through.
As everything in the exposure triangle, aperture has a side effect. It's called Depth of Field. The larger your aperture is opened, the shallower your depth of field will be. (meaning less will be in focus and more will be blurry and out of focus) Using a shallow depth of field is extremely popular in portrait photography.
Coincidentally, the smaller your aperture is opened, the deeper your depth of field will be. (more of your image will be in focus.) A deeper depth of field is often used in landscape photography.
3. ISO
For those who are interested, ISO stands for international standards organization. It is a measurement of how sensitive your camera is to light. A low ISO like 100 means your camera will be less sensitive to light, while a high ISO such as 32,000 indicates a high sensitivity to light. In short, the lower the number, the darker the image and vise versa.
The side effect of ISO is noise. That nasty thing in your image that appears as red or dark colored dots that ruin the detail of your photo. Noise is one of my biggest pet peeves when it comes to photography, and I always try to keep my ISO below 400. Depending on your camera, you may be able to go higher than that and be perfectly fine, I can sometimes go to ISO 800 and be okay if there is sufficient light. But I find that my camera (Nikon D5200) does not preform well at all in low light situations. I have found that Canon DSLRs actually preform a bit better in low light than Nikon. So if you're looking for a camera to use in low light, Nikon may not be the best brand to turn to. (Although it pains me to say so...sorry Nikon) Of course, I'm sure there are Nikon cameras that perform very well in low light, I refuse the believe that there aren't--they are just few and expensive.
