Carbon get into the atmosphere by fossil fuel emissions and respiration. The more carbon dioxide in the atmosphere makes the planet warmer. Then it travels to a land plant or into the ocean.
Once the carbon had traveled into the land plant it is used with the Sun's energy for photosynthesis to create nutrients for itself. Then the plant can release carbon back into the atmosphere with respiration or it can go into the soil
When a plant dies the carbon it stored goes into the soil making it a detritus. Then if fungi or bacteria breaks down the detritus it will go back into the atmosphere. But it can also travel into the ocean.
Carbon can get into the surface ocean by diffusing, circulation, or decomposing which is how it get here. The ocean absorbs more carbon than land does and then the carbon travels into the marine life living in these oceans
Once the carbon travels from the surface ocean certain marine organisms called phytoplankton use the carbon in photosynthesis to create nutrients for itself. So marine life needs carbon to survive but too much carbon in the oceans can be harmful to the creatures.
Then the carbon gets to the deep ocean from decaying organisms or from the surface ocean. If the carbon travels to the deep ocean it will be staying there for hundred of years. Also the deep ocean holds 65% of Earth's carbon. Then the carbon could travel back into the atmosphere through respiration starting the process all over again.