A chemical process called hydrogenation can turn vegetable oils into solid fats, which are then referred to as trans fats. These "man-made" solid fats should be carefully avoided: a good goal is 0-1% of your calorie intake from these fats.
Trans fats are clearly not a healthy fat and will raise the LDL (bad cholesterol) levels in the blood and increase your risk for heart disease and stroke. They're also associated with higher risk of Type II Diabetes.
Foods that contain trans fat include some snack cakes, cookies, icings, stick margarines, pie crusts, popcorn and tortillas. Be sure to check the ingredient label for "partially hydrogenated oil" in order to avoid "hidden" trans fats.