Carbon cycles as CO2 in the atmosphere, enters plants through photosynthesis and exits plants and animlas through respiration.
Dead plants and animals become dead organic matter (DOM) in the soil or water. If the DOM is abundant and left long enough (many millions of years) it becomes a fossil fuel (Which kind of fossil fuel depends on time and surroundings). In the past few hundred years man has removed fossil fuels to provide power. This requires the fuel to be burnt giving off CO2 into the atmosphere.
CO2 is also released into the atmosphere when soil is ploughed for agriculture.
There is a large sink of dissolved CO2 in the oceans, but this is offset by CO2 release back into the atmosphere. This part of the cycle is perhaps the least understood.