Carbon sequestration refers to the portion of the carbon cycle whereby carbon is captured and stored, or sequestered into carbon sinks. The primary short-term (on geological timescales) carbon sinks including biomes, soils, and oceans interact with one another and the atmosphere to absorb CO2. In forests, as trees grow they convert CO2 into carbon to build biomass. When wood burns the carbon is released as CO2, which becomes available for growing trees.
The carbon cycle involves the constant interaction of these sinks and the atmosphere in a dynamic equilibrium that maintains a balance of sorts over time. The long-term sinks include fossil fuels and are part of a process that operates much more slowly in nature than the short-term cycle. When we burn fossil fuels, we release carbon that had been stored for millions of years and in so doing enrich the system causing CO2 levels in the atmosphere to increase.
(CC Image by US DOE [Public domain or Public domain], via Wikimedia Commons) (Click to enlarge)
A partial solution to sequestering this excess CO2 is to manage landscapes to absorb more carbon. This can be done in part by growing trees and protecting those and other forests. Although only a partial solution, carbon sequestration strategies are favored by many in the conservation community and many projects have been developed.
Oceans have been taking up much of the excess CO2 and are acidifying as a result. This has lessened some of the atmospheric changes, and is thought to be responsible for the recent apparent "pause" on climate change. The need to lower our greenhouse gas emissions, as cited by the Intergovernmental Panel on Climate Change (IPCC), should be our top global priority given their predictions of a 2 degree centigrade increase in global temperature.