The photo looks like a type of Liverwort (Marchantia polymorpha), which is probably one of the most primitive true plants alive today.  Liverworts are often found growing in excessively moist areas.              

There are thousands of species of liverwort.  Most weedy liverworts grow flat on the ground and are thallose, meaning their tissues are not differentiated into stems and leaves.  These plants have tissues that are dull green in color, ribbon-shaped, with lobed to forked margins.  Plants often grow together forming a thick mat.  Reproduction occurs by releasing spores into the air and through vegetative reproduction.              

Liverworts can grow in areas of poor fertility, poor drainage, compaction, shading from trees, and high soil acidity.  Alleviating these conditions will discourage the growth of liverwort.  There are really no pesticides to control liverwort.  However, some homeowners have used vinegar with good success.  Liverwort may be removed by raking the areas really hard.