Terraforming (literally, "Earth-shaping") of a a planet, moon or other body is the process of deliberately modifying its atmosphere, surface and ecology to be similar to those of Terra to make it surface more suitable for Terran organisms.  The concept of terraforming developed in SciFi by Jack Williamson in a science-fiction story ("Collision Orbit") published during 1942. Terraforming is often used as a blanket term for all methods of making a world more suitable for life. Closely related to terraforming is geoengineering, technologies for controlling the climate, biosphere or other planetary systems or planetary engineering
Strictly speaking it can be divided into ecopoiesis, enabling the formation of a self-sustaining biosphere, and full terraforming, the transformation of a world into an environment where biologicals can live unprotected. These are two different philosophies of terraforming. The ecocentric approach sought to use natural means to the greatest extent, ideally nudging a planet into a life-sustaining state with a minimal effort and later keeping it there with no need for technological intervention.
The technocentric approach instead would use whatever technology was available to make the world habitable, and did not shy away from installing technological systems to sustain the biosphere. The ecocentrics regarded this as both inherently unstable - what if culture did not sustain the infrastructure needed to keep the planet livable? - and inelegant, possibly even unethical. The technocentrics regarded the ecocentric view as too slow, too mild and likely unable to provide a truly human-habitable biosphere. This dictomy in the philosophies have remained within the terraforming community for centuries, and is likely to remain unreconciled.
The first terraforming project was Mars. Heating up the atmosphere with greenhouse gases, releasing carbon dioxide and water from the regolith, finding ways of introducing plants to create a breathable dense atmosphere, increasing solar influx and so on. In the second and third century of Martian civilization the first  replicators were introduced: genetically modified plants producing fluorocarbons and oxygen, as well as nanotechnological factories digging into the regolith for nitrogen and producing gases protecting against UV radiation. Solar reflectors were aimed at the poles. This terraforming was a mixed ecocentric/technocentric approach, well supported by a large majority of the settlers. It was sometimes violently decried by a minority of environmentalist 'reds' wanting to keep Mars in its native state, but they remained marginal. In 245 ML the first recorded rainfall fell on the planet, and by 380 ML nearly unprotected humans could survive on the surface. Mars was a proof of concept that terraforming could work.
Geoengineering had become necessary in the meantime on Earth, where massive climate disasters threatened billions. Methods for cooling the planet using dust launched into the stratosphere, local heating through space mirrors, weather control and the use of nanotechnological carbon sinks had become commonplace. In a similar fashion the space colonies led to the development of ecodesign, the deliberate construction of stable and productive ecosystems.