Terraforming is the process of reshaping or otherwise modifying the ecology of a planet or moon to make it more habitable for human life. A planet where terraforming fails to "take" and reverts to uninhabitable condition is called a blackrock.
Very few, if any, worlds in the Firefly solar system were entirely suitable for human habitation when colonists first arrived on their multi-generational ships. Atmospheric temperature and composition, among other factors, were usually well outside human tolerances. Colonists can wear space-suits and other environmental hazard gear when outside protected areas, yet they ideally need a more permanent solution to claim a planet as truly their own. Enter terraforming.
In general, terraforming is the process of "tweaking" key traits of a planet or moon to make them more like Earth. This technology is quite widespread in the Firefly universe as characters make reference to terraformed worlds frequently. The exact technology is unknown but is described as taking decades; large machines are seen moving across the surface of a planet undergoing terraforming. Apparently this can even include altering the gravity and sunlight levels of a body by unknown means. As part of the terraforming process, Earthly plant and animal life are also seeded across a world to form a hopefully balanced ecology; types of ecosystems seen include desert, temperate, forest and ocean. Terraforming is also referred to as dangerous work that often kills laborers.
The central planets are much better off than the border planets, possessing much more earth-like environments with easily accessible resources. These inner planets were probably required little or no terraforming to become sufficiently livable. They were the first worlds terraformed, and by the time of the War of Independence have well-established ecologies and industries supporting large populations and cities.
Many border planets face a worse fate. Some of the outer Rim planets are still being terraformed and have harsh conditions and no infrastructure to support human civilization. It often takes more work to get the same results on planets which are more hostile. Also, not all planets react the same way to the terraforming process. "The Train Job" centers on unexpected problems arising from the terraformed moon of a gas giant. This moon thrives solely on its mining industry. Unfortunately, the terraformed surface air mixing with rubble and subterranean air lead to the rise of Bowden's Malady, a degenerative disease which targets muscles and bones. Surprises like this are quite common, with most worlds having a few of their own little quirks.