Organic matter (or organic material) is matter that has come from a recently living organism. It is capable of decay, or is the product of decay; or is composed of organic compounds. There is not one definition of organic matter only. It varies upon the context, the subject it is being used for.
Soil is composed of minerals and organic matter, as well as living organisms. The organic matter in soil comes from plants and animals. In a forest, for example, leaf litter and woody material falls to the forest floor. This is one kind organic material. When it decays to the point it is no longer recognizable it is called soil organic matter. When the organic matter has broken down into a stable humic substances that resist further decomposition it is called humus. 
The equation of "organic" with living organisms comes from the now-abandoned idea of vitalism that attributed a special force to life that alone could create organic substances. This idea was first questioned after the abiotic synthesis of urea by Friedrich Wöhler in 1828.
- Thus soil organic matter comprises all of the organic matter in the soil exclusive of the undecayed material (http://soils.usda.gov/sqi/concepts/glossary.html Archived 2006-11-08 at the Wayback Machine).