The fuel filter's purpose is to filter out dirt or debris while maintaining the required rate of fuel flow. All engines require fuel to make them run, and in precisely metered amounts, therefore anything that impedes the flow of fuel can cause poor starting or running issues.
The fuel injection systems on modern engines have incredibly tight tolerances, so are easily clogged, and any contamination can prove costly to rectify. That's why it's important to replace the fuel filter regularly.
Older engines, especially carburetor-fed ones, are less fussy when it comes to fuel because the jet openings are much bigger than a fuel injection nozzle. But if you get a clogged, or blocked fuel filter you'll still experience problems, so neglect it at your peril. On a car with a carburetor, a clogged filter often manifests as a loss of power or stumble after some minutes of freeway cruising.
There is also the issue with water contamination in diesel engines. Since diesel fuel floats on water, and doesn't mix, many diesel vehicles' fuel filters have a drain tap at the bottom of the housing that allows water to be drained off.
There are two main types of fuel filter, both of which work in the same way: fuel is passed through a filtration medium (often made from a special paper) that catches any contamination.
Some filters are simple plastic or metal containers, with two fuel line connections, around a filtration medium. These are meant to be replaced, not serviced. The other type is a cartridge-style with a replaceable filter housed within a metal container that can be opened.
Bear in mind that many newer cars don't actually have a filter and simply rely on a strainer that's attached to the fuel pump, both located in the tank. These are only meant to be replaced if the pump goes bad. So if you can't find yours – don't panic!