What does a catalyst actually do?
A catalyst speeds up a chemical reaction without being consumed by it — and the mechanism is more specific and more interesting than "it helps the reaction along".
The core idea: activation energy. Most reactions that are energetically favourable still do not happen quickly, because getting from reactants to products requires passing through a high-energy intermediate arrangement — the transition state. The energy needed to reach it is the activation energy, and it acts as a barrier.
A catalyst provides an alternative reaction pathway with a lower activation energy. More molecular collisions have enough energy to clear the lower barrier, so the reaction proceeds faster at the same temperature.
What a catalyst does not do, and this is the crucial correction:
It does not make an unfavourable reaction favourable. Thermodynamics is untouched. If the products are higher in energy than the reactants, a catalyst will not change that.
It does not change the equilibrium position. It speeds the forward and reverse reactions equally, so you reach the same equilibrium faster — never a different one.
It is not consumed. It participates and is regenerated, which is why tiny quantities transform large amounts of material.
The types:
Heterogeneous — in a different phase from the reactants, typically a solid surface with gases or liquids flowing over it. Reactant molecules adsorb onto the surface, which weakens their bonds and holds them in favourable orientations. A car's catalytic converter works this way, and its platinum-group metals are why it is worth stealing.
Homogeneous — same phase, forming intermediate compounds that then break down and release the catalyst.
Enzymes — biological catalysts, and extraordinarily good ones, accelerating reactions by many orders of magnitude with high specificity because the active site is shaped for one substrate.
Catalysts can be poisoned — a contaminant binding to the active site and blocking it, which is why leaded petrol destroyed catalytic converters.