Hydrogenation is the chemical process by which liquid vegetable oil is turned into solid fat. Partially hydrogenated oils contain trans fatty acids, or trans fats, which are thought to be more harmful than saturated fats. Trans fats raise levels of bad cholesterol and lower levels of good cholesterol. You can read more on this in my profile of trans fats.
When liquid vegetable oil is fully hydrogenated, however, almost no trans fats remain. The resulting fat is even more solid, taking on a hard, waxy consistency, even at room temperature. Full hydrogenation increases the amount of saturated fat, although much of it is in the form of stearic acid, which is converted by the body to oleic acid, a monounsaturated fat, which doesn't raise levels of bad cholesterol. This makes fully hydrogenated fats less harmful than partially hydrogenated fats.
When Crisco introduced its trans-fat free shortening in 2004, it contained fully hydrogenated cottonseed oil, which was blended with sunflower oil and soybean oil to soften what would otherwise be a too-hard fat. This particular formula was discontinued as it was relatively expensive. Now, Crisco uses soybean oil, fully hydrogenated palm oil, and partially hydrogenated palm and soybean oils. To be clear: just because it is trans-fat-free doesn't mean it is low fat. One tablespoon of trans-fat free shortening contains 110 calories, 12g of fat, 3g of which is saturated. It is cholesterol free, however.
Beware: if a package simply lists "hydrogenated oil," without expressly stating whether it is partially or fully hydrogenated, it may not be trans-fat free. Sometimes the terms "hydrogenated" and "partially hydrogenated" are used interchangeably. If the package clearly states that it contains fully hydrogenated oil, then it will be trans-fat free. Since stricter labeling laws came into effect, trans fats are more transparent than they used to be, and many food manufacturers continue to look for healthier alternatives for their products.