Catalytic converters are the part of the exhaust system that help to reduce emissions by removing harmful pollutants from exhaust gas as it passes from the engine and out the car. When the converter fails, these pollutants can escape into the atmosphere. This is bad for the environment and it will be a red flag when you take your vehicle to get inspected.
A clogged converter, the most common way it can break down, is difficult to diagnose without removing it from the vehicle and taking it apart. However, one way to check can be to remove the oxygen sensor and see if that alters the vehicle's performance. A sign that you may notice when the converter begins to fail is that the vehicle has trouble accelerating. When the part is partially plugged up, it can limit the engine's RPMs. Once fully clogged, it will be difficult to keep the engine running.
It is important to address a clogged catalytic converter as soon as possible. The noxious gases that are unable to escape through the exhaust pipe can cause damage to the engine and present a real danger to you and your passengers.