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In nature
Carbon sequestration is part of the natural carbon cycle by which carbon is exchanged among the biosphere, pedosphere, geosphere, hydrosphere, and atmosphere of Earth.
Carbon dioxide is naturally captured from the atmosphere through biological, chemical or physical processes.In climate change mitigation
Carbon sequestration - when acting as a carbon sink -  helps to mitigate climate change and thus reduce harmful effects of climate change. It helps to slow the atmospheric and marine accumulation of greenhouse gases, which are released by burning fossil fuels and industrial livestock production.Carbon sequestration, when applied for climate change mitigation, can either build on enhancing naturally occurring carbon sequestration or by applying artificial carbon sequestration processes. 
Within the carbon capture and storage approaches, carbon sequestration refers to the "storage" component. Here, artificial carbon storage technologies are applied, such as gaseous storage in deep geological formations (including saline formations and exhausted gas fields), and solid storage by reaction of CO2 with metal oxides to produce stable carbonates.For carbon to be sequestered artificially (i.e. not using the natural processes of the carbon cycle) it must first be captured, or it must be significantly delayed or prevented from being re-released into the atmosphere (by combustion, decay, etc.) from an existing carbon-rich material, by being incorporated into an enduring usage (such as in construction). Thereafter it can be passively stored or remain productively utilized over time in a variety of ways. For instance, upon harvesting, wood (as a carbon-rich material) can be incorporated into construction or a range of other durable products, thus sequestering its carbon over years or even centuries.
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