Exposure is the amount of light that you allow for your camera to capture. I believe you better are able to understand something if you are told a story line around that subject. In this case there is no need of a story, but the history of it.
The first cameras has film instead of sensor which was a band of plastic on coated with light sensitive chemicals. These chemicals react to the amount of light that are exposed to. So if, for example you expose the film long enough, it will be bombarded by so many photons that in the end you get en entire white photo. If you let it for to little time, there will be insufficient photons to change the chemicals, and you will get a black photo. In order to get a proper photo, you will have to expose it properly, not to let in too much light, but not to less light. The exposure triangle refers to the three factors that control the amount of photons into your sensor: Aperture, Shutter Speed and ISO.
In my last post about Aperture, I have explained how to control the amount of light by means of diaphragm. It is the same principle with a cat eye, for example.
ISO is the sensitivity of the sensor or film. In simple terms, increasing or decreasing the value will help you adapt to the light conditions. When you increase it, the sensor will be more sensible and try to catch more photons. The limitation with ISO is the level of grain that is increasing same time with increasing the value of ISO. Film ISO is usually 100, 200 and 400. Digital cameras have ISO ranging from 100 to 25000 ! For clean images I try to stay below 1600 ISO for digital. In case of film I find the range 100-400 to be sufficient clean for my taste. For example below see that ISO 6400 significantly introduces more noise in the dark area inside the arch.
Shutter Speed works in the same way as Aperture. It controls the amount of photons entering the camera sensor by adjusting the time window the diaphragm is open. Common speeds found on camera settings are 1/15 1/30 1/60 1/125 1/250 1/500 seconds. For hand held photos with film camera, do not have lower than 1/60 of a second as it will appear to be shaken. For Digital cameras with stabilization you can take photos even at 1/20 of a second. In the example below, maybe not the best example as there are shot at different moments in the evening, see that at 5 seconds time window, the water is more glassy and the waves have disappeared.
All three of them are the giving a photographer abilities to take photos for varying light situations and artistic creation. This triangle offers a way to compensate one to another in order to get the desired exposure, as when you have poor light situation, you can increase ISO or slow down the shutter speed, or work on both if you want. When there is to much light you can decrease ISO and increase shutter speed. As an extreme example, if you want the effect of a water flowing during a sunny day, you would need a slower shutter speed, a low ISO, and a small Aperture like f16.
The best way to measure the exposure is by using the Histogram tool. This tool is the most accurate, as you can’t rely on the image you see on the screen from the back of your camera.