Air filters are basically assemblies of pleated paper supported by a layer of fine mesh which can sometimes be made out of nylon or wire that resembles a screen. The screen provides the paper with some strength and also helps to filter out the extremely large particles such as leaves and big chunks of dirt.
Again your air filter may vary but it will have some kind of thick plastic or rubber like gasket material on the ends of the filter. This thick silicone or plastic like gasket also add strength to the automotive air filter and assures a good seal so that all air is filtered through the paper before it enters the intake manifold.
On some vehicles checking air filters is an easy operation. On the other hand some vehicles make it very difficult to remove the air filter for inspection. Check your auto repair manual for the procedure as well as the recommended guidelines for inspection and replacement.