Transition elements are good catalysts because they have multiple oxidation states?Why multiple oxidation states matter?
The answer has a lot to do with "what is a catalyst in the first place?" A catalyst is a compound that can affect the rate of a chemical reaction by providing an alternative and lower energy profile or pathway. That is, it is a substance that makes it so that A -> B at a lower energy cost. But it only has an effect on the rate of the reaction. That is, it only changes the cost of the activation energy. It is not related to the thermodynamics of the process and hence, the final product distribution. That is, if the above process gives 90% B via a non-catalyzed pathway in 4 days, then a catalyst will help you get 90% B in say 4 hours.
Okay, so a catalyst affects the transition state and activation path. How does it do this? Typically, by complexing one of the reagents. Complexation by transition metals affords access to a wide variety of oxidation states for the metal. This has the property of providing electrons or withdrawing electrons from the transition state of the reaction. That is, if the transition state is electron rich, then the transition metal might hold some of that electron density and those prevent too much from building up on the reagent. This would then facilitate the reaction. Or the transition metal might undergo formal oxidation/reduction to achieve electron transfer to a substrate, thereby allowing a reaction to occur. This is "complexation and electron storage" taken to the extreme but is a common mechanism in organometallic chemistry. Indeed, a variety of catalytic pathways rely on a two electron transfer between the metal and the substrate (e.g. hydroformylation). It is the ability of the transition metal to be in a variety of oxidation states, to undergo facile transitions between these oxidation states, to coordinate to a substrate, and to be a good source/sink for electrons that makes transition metals such good catalysts.
Of course, this is for transition metal complexes. Most industrial used catalysts are the transition metal in a bed, as a metal or bound structure. The above considerations are important but also the physical properties of absorption/adsorption and the electron band structure of the material.