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Firstly, let me define a catalyst and how they work:
thEy work by increasing the frequency of collisions between reactants and allowing them to keep their physical or chemical properties. Catalysts affect the rate of reaction without affecting the thermodynamics in a system, thus provide an alternative, low energy pathway for a reaction toproceed. A catalyst affects the transition state of a reaction by providing the transition state a lower-energy-activation path. Here is a diagram explaining this.
Now to answer your question, I think this is because they can carry various charges. A good example is Manganese (Mn). It can carry up to 6 different charges: +2, +3, +4, +5, +6 and +7. Similarly, iron (Fe), a very important transition metal that plays a huge physiological role in our bodies by helping us carry oxygen through our blood, can hold either +2 or +3 charge. What does this mean? Well, it means that they can act as good electron donors and acceptors easily, making them very easy to act as catalysts to use and re-use.