Without biochar
Carbon dioxide is pulled from the air by plants, dissolves in the oceans (which creates problems), and (slowly) absorbed by weathering minerals. When those plants rot, carbon dioxide goes back into the air. The rotting process also produces methane.
Humans have created massive sources of carbon dioxide, which add it to the atmosphere faster than natural processes can remove it.
With biochar
Some of the carbon from the biomass is converted to a form - charcoal - that does not biodegrade. This carbon is removed from the carbon cycle, essentially permanently.
