Nothing Lost
No chemical is ever considered to be lost in a biogeochemical cycle. Sometimes the chemical may be held somewhere for a very long time, such as the carbon that is in coal deposits deep in the earth, but it is still there. That kind of holding place for a chemical is called a reservoir, and they are generally non-organic. Exchange pools are the steps of the cycle that don't last very long; they are usually organic. Given enough time, all chemicals will cycle through both organic and inorganic factors.
Chemicals of Life
The kinds of chemicals that are studied in biogeochemical cycles are ones that are used by living organisms. They include oxygen, nitrogen, carbon, phosphorous, sulfur and water. Following the progress of a single chemical through air, earth and organism illustrates the connectivity of nature and the dependence of living beings on their environment and vice versa. It also illustrates the point the recycling is a fundamental principle in nature.
The Water Cycle
One of the easiest biogeochemical cycles to explain is the water cycle, or hydrological cycle. First, water vapor in the atmosphere condenses into liquid due to cold temperatures. It falls to the earth as rain and either soaks into the ground or runs off into rivers. Great heat causes the liquid to evaporate, or turn back into a gas. You can also add to that the water absorbed by plants and drunk by animals, which returns eventually by way of drying up, sweat, urine and other means.
The Carbon Cycle
Carbon dioxide is the gaseous form of carbon which fills our atmosphere. It is absorbed by plants through photosynthesis and used to make carbon-based plant food. When those plants get eaten, the carbon passes onto that animal -- or else they decay, and the carbon goes into the ground. From one animal, the carbon may pass onto another animal by eating and eventually will either be breathed out in the form of carbon dioxide, or it go into the earth when the animal dies. The stored carbon in organic matter can turn in time into coal, to be released only when it gets dug up and burned.