Organisms that take part in decomposition break down organic matter into nutrients that are used in the nutrient cycle.
There are a variety of organisms which take part in decomposition, from Vultures to Bacteria, from Fungi to Grubs, they all feed on the decomposing material, often varying what they feed on to what they're adapted to, for example Vultures often take part in decomposition of animal material (carcasses), Fungi on plant material (dead trees) and Bacteria on feces (poo).
Most organisms that help in decomposing, decompose more than one type of organic material, which helps speed up decomposition of organic matter in global environments, (just don't expect to see Vultures chowing down on dead plant material).
The nutrients that come out of these products, such as carbon dioxide, water, nitrogen, phosphorus, potassium, calcium, magnesium, and sulfur, the latter 6 being used by plants in growing and reproduction.
Organisms which decompose organic material help use keep our world tidy and disease free, but also help to recycle the minerals in ecosystems and help to create new life for animals and plants to flourish in.
Hope this helps.