Basically you have three kinds of fats. Saturated fats are the ones you find in meats, dairy, etc..essentially these fats are solid at room temp and the name saturated means that on a chemistry level, all the available bonds are attached to hydrogens. All the bonds in the compound are single bonds. This is partially why they are solid at room temp. The second type is unsaturated fats. These are all veggie fats like corn oil, olive oil, etc. and they are liquid at room temp. Basically these fats are unsaturated because some bonds are double or triple. More hydrogens could be added if those extra bonds were broken.
Hydrogenated or trans fats are the third type. These are bad for a number of reasons. First they do not exist naturally. What has happened on a chemical level is that double and triple bonds have been forced apart and more hydrogen has been added to the compound. This is usually done to make the fat more solid at room temp (think margarine). The body reacts badly to these fats because they are unnatural. The body doesn't quite know how to handle them so they have a huge negative impact on HDL and LDL levels, and huge impact on triglycerides too. Studies have also shown a small increase in the risk of breast cancer and other cancers.