The exchange of carbon between the ocean and atmosphere and the biosphere and atmosphere is known as the fast carbon cycle. During this cycle, a lot of carbon is exchanged over a relatively short amount of time.
The slow carbon cycle refers to carbon flux within rock. The atmosphere can put carbon into rock through rain—rain in the air can dissolve carbon dioxide, which then falls onto the Earth, which can absorb some of it in soil. A lot of this rain ends up in rivers, which then end up in the ocean. Oceans can put carbon into rock because over time, shells of dead life forms in the ocean cement together to form rock known as limestone. Under pressure of the Earth, limestone can form other minerals such as marble.
The terrestrial biosphere also puts carbon into rock. Dead things from the terrestrial biosphere are buried and compressed within the Earth to form various types of rock, such as shale. If dead life forms builds up under the pressure of the Earth faster than it can decay, they form fossil fuels. Fossil fuels are coal, oil, and natural gas.
Rock can release carbon through the shifting of tectonic plates, which can cause volcanic eruption. Just like other carbon cycles, the slow carbon cycle that occurs in rock eventually releases about as much carbon as it takes in, but the process takes place over hundreds of millions of years. On a yearly basis, the slow carbon cycle account for about 1-10 gigatons of carbon released from rock by volcanoes and stored in rock by Earth processes.