Step 1: Electron flexibility.
The hallmark of a transition metal is a partly filled d-subshell whose electrons are easy to add or remove. This lets the metal switch oxidation states during a reaction, opening a fresh, lower-energy route for the reactants and thus speeding the process.
Step 2: Intermediate stage.
Because of these accessible states the metal briefly bonds to a reactant, forming an intermediate that reacts more easily; once product forms, the metal returns to its original state, so it is not consumed.
Step 3: Surface action.
In heterogeneous catalysis the vacant or partly filled d-orbitals adsorb reactant molecules onto the metal surface (as with Ni, Pt, Pd), holding them close together and stretching their bonds so they react faster.
Step 4: Example.
Finely divided iron in the Haber process (\(N_2 + 3H_2 \rightarrow 2NH_3\)) works both by adsorbing the gases and by using its variable oxidation states.
Conclusion: The combination of variable valency, intermediate/complex formation, and strong adsorption on d-orbitals explains their catalytic power.
\[\boxed{\text{d-orbital adsorption + variable valency = catalysis}}\]