To dumb it down into the very basics. A new tank, whether you go the "fish in" route, or just add ammonia/fish food/shrimp, whatever, will start to produce ammonia as the first part of the cycle. Ammonia is extremely toxic, even in very low ppm's.
Fortunately there is a bacteria, nitrosomnas, which eats the ammonia rendering it safe, but....a by product of this process is nitrite, which is just as toxic as ammonia, so we're back to square one.
However, we have another friendly bacteria, nitrobacter, which eats the nitrite and the end product of this is nitrate. Nitrate is far less toxic than the other two, but long term, it can cause problems. Nitrate and fish is like cigarette smoke and humans. It's a slow burner.
This is where the cycle ends in our aquariums. We don't have another friendly bacteria to eat the nitrate*. So what do we do now? Well the nitrate, over time, will gradually rise, quickly if you are overstocked and/or feed heavily. Slowly if you are understocked and feed lightly. It's what we call "bio load".
This is where water changes come into the equation. We must dilute that forever rising nitrate. And that's as dumbed down as I can put it.
*There are other bacteria that do indeed eat nitrate, but not in the usually oxygen rich closed loop environment that our aquarium set ups offer. This method of nitrate reduction is very complex.