The fuel filter helps prevent the sediment from the bottom of your fuel tank and other contaminates from clogging your carburetor or fuel injectors. When the fuel filter gets old and dirty it may clog up preventing fuel from flowing through it properly. Symptoms of a dirty fuel filter include hard starting, poor fuel economy, hesitation, or loss of power, particularly at higher loads (such as when trying to accelerate while climbing a steep hill), when fuel demand is higher. A clogged fuel filter can make the pump work harder, potentially leading to early fuel pump failure, an expensive repair.
There are several ways to check the fuel filter, but the easiest is to figure out when it was last changed. Fuel filters are relatively inexpensive and easy to change, so if it has been longer than the manufacturer's recommended replacement interval, it is probably best to just change it. You can also preform a visual inspection of the filter. Some filters will have a window that let you see inside the filter, if it looks dark, dirty, or gummed up, it should be replaced. If there is no window you can still take a look at the outside of the filter and check its condition. If it is rusty or looks like it has been on the vehicle for a long time, consider a replacement.