All cars have an air filter. Its job is to trap the dust, debris and particles that could otherwise damage the engine if they got sucked into it.
They are commonly situated in a large plastic box to one side of the engine bay between the air inlet and the engine itself so that air entering the engine will first have to pass through the filter first.
Virtually all air filters you're likely to find in a production car will be made out of paper, although it's not like a sheet of A4 - it's much thicker for a start off, plus it's more permeable, allowing air to flow through it with minimal restriction.
The paper is folded concertina-style to maximise the surface area. This allows it to let the maximum amount of air through it, while at the same time providing a large surface area with which to trap the dust and debris.
Around the paper 'core' you'll find a soft foam gasket. This, commonly orange, gasket helps create an airtight seal within the air filter housing ensuring no unfiltered air sneaks into the engine!
Most filters are rectangular, but it's not uncommon to find cylindrical filters. They operate in exactly the same way, and often feature the gaskets at both ends of the cylinder.
Performance air filters, filters on high end sports cars are more likely to use foam as the filtration media, as opposed to paper.
The thinking behind this is that foam is less restrictive, and so allows more air the engine, albeit at the expense of filtering out the smallest of particles.
Eventually the filter will become so dirty that it will no longer flow sufficient air, and will need to be replaced. This is usually done at a vehicle's annual service.