The two major classes of catalysts are homogeneous catalysts and heterogeneous catalysts. The homogeneous and heterogeneous refer to the state of the catalyst compared to the state of the substances in the reaction. For example, a heterogenous catalyst might be a solid which is catalyzing a gas phase reaction. For a homogeneous catalyst, one could have an aqueous reaction with an aqueous catalyst.
We have catalyzed reactions going on in our body every day. As the body processes the food we eat, it uses enzymes as catalysts. A common example of this is lactose (a sugar) and lactase (an enzyme). For those that are lactose intolerant, they lack enough lactase to process the lactose. Without the enzyme, the reaction does not happen efficiently and an alternate chemical reaction occurs resulting in gastric distress.