The act of modifying the atmosphere, soil, and climate, of a planet, typically to make it more habitable (or just more comfortable) for human colonization.
Generally this requires creating a breathable atmosphere with a comfortable climate and adding life to create a functioning ecology. One of the best tales of terraforming is the RGB MARS trilogy by Kim Stanley Robinson.
Of course, terraforming, as with most engineering concepts, is marked by trade-offs. For example: Releasing more CO2 into the Martian atmosphere will increase the greenhouse effect, and therefore the temperature of Mars. This in turn will liberate more CO2 from the regolith and polar ice caps, thereby increasing warming, and adding to the atmospheric pressure. This will make it easier to work on Mars, but CO2 is also a deadly poison to humans at any large concentration in the atmosphere. So if your ultimate goal is an earth-like world, the CO2 will be a problem.
An excellent discussion of possible methods for terraforming mars can be found in Robert Zubrin & Richard Wagner's The Case for Mars (ISBN: 0684835509)
The term terraform also refers to training a planet to go and fetch beers for you, however this latter definition is silly, and is not in common usage.