Many branch at the base and produce more or less equal sized stems called tillers. The leaf has a blade and a sheath that surrounds the stem or culm. The regions where the leaves originate are called nodes. See the diagram on pg. Horizontal stems that grow along the ground are called stolons.
Vegetative reproduction is common in perennial grasses.
Grass floral structures are even more complex. Most grass flowers are perfect. Grass flowers are borne in compound infloresences called spikelets. A floret is an individual grass flower. There is a superior ovary topped by two feathery stigmas.