All living things contain carbon. Remember the equation for cellular respiration--oxygen + carbohydrates--->carbon dioxide + water (and releases energy). The reverse, photosynthesis, is the way that energy is captured as sunlight, and made available for living things. Both carbohydrates and carbon dioxide contain carbon.
Carbon is also found in various other compounds in our bodies, such as proteins, lipids, and genetic material. It helps make up our teeth and bones. When carbon cycles, it also does so through non-living things. The amount of carbon does not change; we can't get more. If carbon did not cycle through various forms, there would not be any available for living things, and life would not be possible. At least, not any type we are used to.