A catalytic converter consists of a stainless-steel casing that houses a metallic (metalith) or ceramic (monolith) substrate or core. This substrate has a very large number of fine channels running through it along its entire length (like a honeycomb), which increase the active surface area available to support the catalyst, which explains why it is also often called a "catalyst support".
The surface of the substrate is coated with a highly porous "washcoat" (which forms a rough, irregular surface that gives the substrate an even larger surface area) to which precious metals (platinum, palladium and rhodium) are added in suspension. It is these precious metals that are the actual catalysts that initiate the chemical reactions that reduce the levels of pollutants in the exhaust gases.
To produce this mixture, the lambda sensor screwed into the exhaust pipe between the engine and the cat measures the residual oxygen content in the exhaust gases. The engine management system uses these measurements to compute and output the control pulses to keep the air-fuel ratio at the optimum point.
The cat used in spark-ignition engines performs all three reactions (reduction of nitrogen oxides to nitrogen and oxygen, oxidation of carbon monoxide to carbon dioxide and oxidation of unburnt hydrocarbons to carbon dioxide and water) simultaneously. That's why it's called a three-way catalytic converter.