Mosses (along with the liverworts) belong to to an Order of the plant kingdom called Bryophyta - the bryophytes. (See under Basic Facts for a basic description of bryophytes, and the differences between mosses and liverworts.)

Mosses come in a wide variety of forms, but all are based on a stem and leaf structure. The stem may be branched to a greater or lesser degree. Broadly, they can be divided into two groups - acrocarpous and pleurocarpous mosses.

Acrocarpous mosses usually grow erect, and have a main stem which is of limited growth, and which terminates with an "inflorescence" (a collection of male and/or female sexual structures). Further growth takes place via branches off the main stem. An example of an acrocarpous moss is Bryum pseudotriquetrum.

Pleurocarpous mosses have a main stem of unlimited growth, and usually much-branched. Inflorescences are produced on short branches. An example of a pleurocarpous moss is Hyocomium armoricum.

With experience it is usually a simple matter to tell these two groups of mosses apart, and this is an important early step when attempting to identify an unknown specimen.

For some more information on mosses, and some useful images try this page at Ohio University.