Most cartridges contain a paper filter which works just like a screen filter. Most also remove organics well because the paper texture is rough enough to snag the organic matter. While some cartridges can be washed, most of them you simply replace when dirty. In most cases the media material is uniform sized, crushed sand. The water passes through the small spaces between the media grains and the debris is stopped when it can't fit through these spaces.
Media filters are best for removing organic material from the water.
This is where the importance of the sharp edged media comes into play. These sharp edges snag the organics which would otherwise slime and slither their way through the small spaces. This is why it is important to use sharp media. Media filters are the type of filters most commonly used for high volume cleaning of water from rivers and lakes. They are used by both large farms and municipal water systems.