Mosses have tremendously flexible usage in planted tanks. They are undemanding in terms of light, nutrients and CO2 (suitable for low tech tanks) and can be flexibly placed in the aquarium as they can grow well even without a substrate. This means they can be attached to rock and wood, taking on the shape of the surfaces they cover. There are many varieties of mosses, which gives us a large range of textures to work with.
Beginners tend to avoid mosses as their tanks do not contain much hardscape; but they are a staple of hardscape heavy competition tanks. They allow an aquascaper to fill a tank with hardscape yet retain a planted look by covering hardscape surfaces with moss. Maintaining the form of hardscape focused tanks is much easier with moss than with rooted plants most of the time, which require far more management and pruning.
A few varietals covered here are actually liverworts rather than true mosses, but they all have similar growth requirements and usage.
Top view of tank above
My ADA90p tank planted mostly with mosses and bucephalandra
Right side of tank
Middle of tank
Head here to find out how to cycle a planted tank.