The least known and experimented with portion of the exposure triangle is what we call ISO, or the sensitivity of your camera's sensor. The more you increase this ISO number, the more sensitive your camera is to light, thus allowing more light in. However this comes with a trade off, the higher the ISO the more noise that appears in a photo. Now you ask what is noise?

Noise is what you would call "visual distortion" in a photograph, this resembles a grain like texture. Noise is usually experienced when shooting in low-light conditions (indoors/nighttime). Although there are some instances when it is necessary to increase your ISO in order to achieve an acceptable photograph. Your camera sensor will determine how well low light performance is. Sensors that are larger and more recent will perform better in low light. Hence why you will see full frame cameras being advertised for their excellent low light performance. Noise will remain the same for any given body at each ISO value too, which will allow you to do ISO testing to see at what ISO noise becomes unacceptable.

ISO is linear. Therefore when you double it, the amount of light you allow in also doubles. This makes it easier to determine what ISO value you will want to shoot at. 

Now noise can be removed from photos fairly easily, there are multiple softwares that can accomplish this. Even Lightroom can accomplish this fairly well, but this doesn't come without consequences. When you remove noise you are also removing fine details from an image and essentially "smoothing" it out. 

All cameras have what is referred to as base ISO, which is the optimal ISO for best image quality. This number is usually 100 but can be even lower given the body. Some cameras can go below base ISO down to 50 (if base ISO is 100) which can be used if you are trying to slow down your shutter speed for a longer exposure.

Here are some cases where increasing ISO makes sense: shooting the milky way, nighttime street photography, portraits at night or indoors (without proper lighting equipment), and indoor architecture photography where using a tripod isn't viable. Now there are many more cases but these are just a few examples. 

Remember that ISO needs to be balanced with both shutter speed and aperture. Shooting at the lowest ISO you can should usually be the goal. This will end our series on the exposure triangle. Now that have knowledge on the elements you should try to shoot in manual mode and practice, this is the best way to learn. Practice makes perfect (ok not really but you'll definitely improve).

Stay true to you.