transition-metal catalysis
Some of the hardest reactions in organic chemistry, especially joining two carbon fragments together, are made easy and clean by a tiny amount of a transition metal like palladium, nickel, ruthenium, or rhodium. Transition-metal catalysis is the broad idea of using such a metal to speed up and steer a reaction, while the metal itself is regenerated and reused at the end, so a trace amount can transform a flask full of material.
What makes transition metals special is their partly filled d orbitals, which let them temporarily form, break, and rearrange bonds to carbon in ways no main-group element easily can. A catalytic cycle is built from a handful of recurring elementary steps: oxidative addition (the metal inserts into a bond, such as a carbon-halogen bond, raising its oxidation state), ligand exchange / transmetalation (groups swap onto the metal), migratory insertion (a group slides onto a coordinated alkene), and reductive elimination (two groups on the metal couple together and leave, forming the new bond and returning the metal to its starting state). The metal acts like a molecular workbench: it grips both pieces, brings them together in just the right geometry, helps them bond, and then lets go, ready for the next cycle. Crucially, a catalyst lowers the activation energy and so speeds the reaction; it does not change the position of equilibrium, only how fast that point is reached.
Transition-metal catalysis revolutionized synthesis, above all by making carbon-carbon bond formation routine through the palladium cross-coupling reactions and olefin metathesis. It also underlies catalytic hydrogenation and a huge swath of industrial chemistry and pharmaceutical manufacturing. The recurring message is leverage: a sub-stoichiometric pinch of an expensive metal, by cycling over and over, accomplishes a transformation that would otherwise be slow, dirty, or impossible.
In a palladium-catalyzed coupling, Pd(0) does oxidative addition into an aryl-bromide bond, then a series of steps, then reductive elimination forms the new C-C bond and spits out Pd(0) again, ready to start another cycle.
The metal cycles through oxidative addition and reductive elimination and is regenerated.
A catalyst speeds a reaction by lowering its activation energy and is regenerated, but it does not shift where the equilibrium sits, it only helps the system reach that equilibrium faster.