Any filter — home, auto, or otherwise — will eventually age and become clogged with pollutants and debris. When that happens, it becomes harder for the air or fuel to continue traveling through the filter, which can cause issues. Eventually the filter media may break, allowing contaminants to reach parts the filter is meant to protect.
When your air filter is clogged and heavily restricts airflow, it may lead to incomplete combustion, and ultimately reduced engine power. In turn, a clogged cabin air filter can lead to under-performance of the A/C system, causing weak airflow from the cabin vents. It can also lead to unwanted, unfiltered air in the cabin.
As for a clogged fuel filter, that can cause a reduction in engine power, low fuel pressure to the injectors, poor acceleration, and lousy fuel economy — not to mention a potential breakdown.