First of all, let us understand we are talking about the recycling of the element carbon within the confines of planet Earth. Earth has a finite amount of carbon, which is essential to all forms of life as we know them, hence the pun "just another carbon-based life form". Since there is a limited supply the cyclic "sink" process is invaluable in harvesting spent carbon and putting it back to work in a different format.
Probably the most invaluable carbon sink that corrals carbon from the carbon dioxide humans give off as they exhale would be the plants, everything on the plant side of living organisms. Plants are instrumental in taking carbon dioxide, combining it with water and a little energy from the sun, and producing their own food supply in the form of the simple carbohydrate, glucose. Oxygen is also produced, in this example of photosynthesis, as a waste product.
Another source of increased atmospheric carbon dioxide is the burning of fossil fuels as an energy source. This has greatly increased the amount of carbon dioxide in the atmosphere, so much so it has contributed to a phenomenon know as global warming. The oceans absorb some of this extra carbon dioxide, as does the soil surrounding the aforementioned plants, already busy doing their part. All these "sinks" help in recycling the element carbon back into the Earth, in reusable increments.