Anything that is alive or was once part of a living organism is organic matter. Oak leaves, a bird's shed feathers, and the limp carrots in your compost pile are all organic matter.
Organic matter is made largely of carbon-containing compounds that come from living sources. It naturally decays over time and becomes part of the earth. Dead insects, animal waste, fungi, and even human bodies are organic matter. It's a vital part of the cycle of life, adding necessary nutrients to the soil so that new plants can grow. Although we often use the word organic to mean "natural" or "healthful," scientifically speaking, organic matter refers to carbon-containing material associated with living organisms.