Every form of recorded light revolves around these three settings on your camera. Master them and you'll never again have to wonder "why didn't my shot come out"
The Exposure Triangle is a fancy name for the three factors which affect how a camera takes an image; these are shutter speed, aperture, and ISO. If you leave your camera in Auto mode then you're allowing the camera's computer to make all the setting decisions, and they can't always be relied on to make to right choices. Understanding how each of these settings affects the final image is vital to taking better photos.
Shutter speed is the length of time that the shutter stays open, exposing light onto the sensor. Remember shutter speed is measured in fractions of a second, so a "higher" number is actually a shorter shutter (1/200 is faster than 1/60). The longer the shutter stays open, the more light is allowed to reach the sensor, however depending on the subject, too long of a shutter will create motion blur. The general rule of thumb is your slowest shutter should always be at least double the focal length of your lens; so a 50mm lens should be shot at a minimum of 1/100, but a 24mm can be used at 1/50. This is to avoid shake caused by simply holding the camera, because the further you zoom, the more exaggerated even minute vibrations will appear, requiring a faster shutter to compensate. Some newer lenses have advanced vibration reduction technology, allowing you to shoot at slower speeds without worrying about lens shake; but this isn't always the case. You also need to consider the movement of your subject in relation to your shutter speed as well; a running athlete will need to be shot much faster than a posed portrait.
The next corner of the triangle is aperture, which is the size of the hole through which the lens allows light into the camera. this affects the image in two ways, the amount of light in the photo, and the depth of field, a term for how much of the image is in focus at the same time. This works the same way that squinting can help your eyes focus on something when your vision is blurry. Aperture is measured in f-stops with higher numbers corresponding to smaller apertures, so something shot at f/11 will have a much larger depth of field than something shot at f/4. This is also how photographers create those images where the subject is in focus and the background is completely blurry. This is known as bokeh, and is accomplished by shooting with a very wide aperture (usually f/2.8 or larger), and often using a telephoto lens, as zooming in on a subject creates an effect called Compression Distortion, which exaggerates the separation between your subject, and background.
The final piece of the puzzle is the ISO setting. ISO is actually fairly complicated, but the simplified explanation is to equate it to the sensitivity of the imaging sensor; thus the higher the ISO setting, the more gain is applied, brightening the image, but simultaneously increasing the graininess of the photo. This is why photos taken in the dark tend to look very fuzzy or gritty; the camera is compensating for the low light by raising the ISO. Most cameras can go as high as 1000 ISO without seriously affecting the quality of the image, but some professional models can handle 3000, and newer mirrorless cameras are shattering that ceiling with effective ISOs of 12800 and higher.
The lighting conditions and subject movement of every individual photograph will require precise manipulation of all of these settings, but learning how they impact the image is imperative to understanding your camera, and developing the ability to take the kind of photos you want to see.