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Fish give off ammonia, and ammonia is quite toxic. Fish waste, and uneaten fish food, is broken down by bacteria, also giving off ammonia. Another bacteria starts growing in the aquarium, and it oxidizes the ammonia into nitrite, then another bacteria starts growing in the aquarium, and it oxidizes the the nitrite into nitrate. Just like it takes time for things to grow, it takes time for bacteria to grow. It is best to give a new tank 1 week with the filters running before you add any fish. Then on a weekly basis you can add fish while also testing your water. For biological filtration, especially in the filter, the more surface area that you have for the bacteria to grow, and the more waterflow going over the bacteria, the better it is. Many filters on the market hang on the back, and have slide in filters that are designed to be changed just like you change a vacuum cleaner bag, but when you throw out the filter, you are also throwing out the beneficial bacteria. This can cause your your fish to get sick, and your water to turn cloudy. The AquaClear filter has a foam block in it that is designed to be reused. Simply give it a quick cleaning to get the dirt out, and put it back in the filter. That way you have gotten dirt out of the aquarium, but the bacteria is still in the foam block. The manufacture recommends changing the foam block every 3 months, or so, but I use them forever.
Down in the sand, and inside live rock, in low oxygen areas, bacteria will take oxygen away from nitrate, and convert it back to nitrite, and take oxygen away from nitrite, and convert it into nitrogen gass, that bubbles up out of the aquarium.
Ammonia (NH3)
Ammonium (NH4) less toxic, occurs more in lower ph conditions
Nitrite (NO2)
Nitrate (NO3)
Nitrogen Gass (N2)
Fresh water plants are also good for removing ammonia from the tank. If they are growing, they take up ammonia, if they are dying, they give off ammonia. In salt water, the seaweed prefers nitrate, and so helps take up nitrate.
Where does nitrogen come from? All food has proteins. Proteins are polymers that contain a variety of elements including nitrogen. Without nitrogen, nothing would live.