The key is the word "compost" and that defines a process of decomposition by microrganisms that generates heat and results in a breakdown of the original ingredients into a relatively uniform, dark, earthy looking material with a rich, earthy (for lack of a better term) aroma. A quality compost is typically comprised of a variety of recycled materials - 'greens' (high nitrogen sources) like grass clipping, old annuals and vegetable remains, kitchen scraps, etc., even weeds; and 'browns' (high carbon sources) like dried leaves, twigs and small pruning trimmings, paper products, straw, etc. Once composted together sufficiently and allowed to age a bit, the resultant product is a well-rounded, organic nutrient source and will add structure, porosity and microbial activity to any garden soil.

Aminal manures can provide similar results, however most should be fully composted or at least very well aged before use in the garden and they tend to be less diverse in terms of nutrient availability.

Check out the Soils, Compost and Mulch forum for ongoing discussions of this topic.