Literally, "Earth-shaping": the process of modifying a planet to a more Earth-like atmosphere, temperature or ecology.
The term was first used in a science fiction novel, `Seetee Shock' (1940?) by Jack Williamson, but the actual concept is older than that. An example in fiction is `First and Last Men' by Olaf Stapledon in which Venus is modified, after a long and destructive war with the original inhabitants, who naturally object to the process. Early fictional accounts of the process are frequently handicapped by the inaccurate contemporary knowledge of the actual conditions, as in the Stapledon example, which had Venus covered in oceans.
A more recent example, using the actual conditions on Mars as revealed by planetary probes, is the Mars trilogy by Kim Stanley Robinson. The three volumes are a lengthy description of the fictional terraforming of Mars, and are very evidently the result of a massive amount of research by the author.
In the 1960s astronomer and popularizer of science Carl Sagan proposed terraforming the planet Venus by seeding its atmosphere with algae, which would remove carbon dioxide and reduce the greenhouse effect until surface temperatures dropped to comfortable levels. Later discoveries about the conditions on Venus made this particular approach impossible, however; there is simply too much atmosphere to process and sequester. Even if atmospheric algae were able to thrive in the hostile and arid environment of Venus' upper atmosphere, any carbon that was fixed in organic form would be liberated as carbon dioxide again as soon as it fell into the hot lower regions.
Today the most feasible planet for terraforming appears to be Mars. A well elaborated plan was presented by Robert Zubrin, the founder of the Mars Society. He wants to start with a Mars return mission called Mars Direct.
The pricipal reason given to pursue terraforming is the creation of worlds suitable for habitation by human beings and an ecology to support them. However, some researchers believe that space stations will be a more economical means for supporting space colonization.
If research in nanotechnology continues apace, it may become feasible to terraform planets in weeks rather than centuries. On the other hand, it may become reasonable to modify humans so that they don't require an oxygen/nitrogen atmosphere in a 1G gravity field to live comfortably. That would then completely obviate the need to terraform worlds.
(this needs a lot more yet, including non-fictional research - and the aspect that the whole problem of greenhouse gases is that we are inadvertantly engaged in the terraforming project of returning atmospheric carbon dioxide to the levels of millions of years ago)