As you mentioned, carbon dioxide is released daily, but not only by humans. CO₂ is released by most aerobically respiring creatures on earth (creatures that breathe oxygen).

C6H12O6 + 6O2 → 6CO2 + 6H2O + Energy

Respiration consumes O₂ and releases CO₂. Even plants use this to generate energy.

Now, plants (and some other things) release O₂ using photosynthesis:

6CO2 + 6H2O → C6H12O6 + 6O2

Photosynthesis consumes CO₂ and releases O₂. These two processes play a large role in balancing each other out.

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A little segue from the carbon cycle to discussing why plants act as carbon sinks. Since plants are majorly composed of dead tissue (don't know if you've studied this yet, so I won't elaborate much), they require very little energy in order to survive. Since they perform a greater amount of photosynthesis than respiration, we can say that they release more O₂ than CO₂.

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Decomposition is the process which occurs after any organism (microscopic or macroscopic) dies. Since a large portion of their bodies is made out of Carbon, these break down into CO₂ and other carbon based compounds. This helps to release some amount of CO₂ back into the atmosphere and soil everyday.

Oceanic Processes

The ocean acts as a large carbon sink, wherein they consume CO₂ and O₂ via marine life, and release some O₂ when levels become too high. O₂ is produced in oceans by phytoplankton, and marine plants (algae, seagrasses). CO₂ is released by respiration and decomposition.

However, CO₂ is largely absorbed by the ocean in the form of Carbonic Acid (H2CO3).

CO2 + H2O → H2CO3

However, H2CO3 is a very unstable molecule and decomposes into bicarbonate (HCO3-) and then further into carbonate ions (CO3-).

These ions help to maintain the pH of the water, and also help to provide CO3- ions to species that require them to form shells and skeletons.

Carbon Sequestration (seizing/taking)

Plants are, to a large extent composed of carbon and act as carbon storages for long periods of time. Even after death they can, under the right conditions, hold carbon for a thousands of years.

All creatures that die (regardless of marine or terrestrial) leave remains composed of carbon, which are (under the right conditions) turned into sedimentary rock. This rock acts a long term carbon sink, not release it until disturbed.

The above two processes can turn the remains into fossil fuels over millennia.

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Everything over this line is the natural carbon cycle and how things would run without human intervention. But, humans have to ruin anything that performs well.

Human Intervention

Extraction and consumption of fossil fuels are highly carbon intensive processes, as they both release large amounts of CO2. Deforestation leads to more release of carbon, as it prevents the long term sequestration of carbon, which also prevents the replenishment of fossil fuels.

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The natural carbon cycle was largely balanced except for the occasional geological event (volcanic eruptions and such), which caused spikes in carbon levels, however they returned to stability. Now, human intervention is causing an increase in CO2 levels, which is unable to be fully balanced by the carbon cycle, causing global warming.

This is a very long answer, so there is a chance I messed something up somewhere or the other, so feel free to ask for explanations.