This is an extremely over-simplified, not-very-scientific explanation of the rather complex nitrogen cycle. Knowledge of the cycle is invaluable in the care of your aquarium.
And that's really about it.
So how does this relate to aquarium care? Well, you can see why partial water changes are needed to prevent the build-up of nitrates.
Understanding water chemistry can help you decide on a schedule of water changes. Testing your water frequently while your tank is new and still building up bacteria will enable you to measure your tank's progress and know when to add new fish or do water changes.