Sessile organisms stay in one place, whereas motile organisms are mobile. The majority of organisms are motile, but many important organisms, including coral, sponges, barnacles, tunicates, bryozoans, polychaete worms, some bivalves, and most brachiopods are sessile. Of course, all land plants stay in one place. Some animals have motile larval stages and sessile adult stages, or vice versa.
Animals that stay in place must use passive feeding methods, specifically filter feeding. Sessile plants use photosynthesis for energy in all except rare cases. Animals have evolved a variety of interesting means for getting nutritious bits out of water, where they almost always live: tentacles, filters, and pumps. Motile animals, which are by far the most common and complex, have a much greater number of available means to obtain food, but at the same time, their nutrient requirements are greater.
Sessile marine organisms have been extremely common since the dawn of multicellular life. Most of the earliest animals, making up an assemblage called the Ediacaran fauna, were sessile. During the Ordovician period, about 480 million years ago, there was a jump in the number of filter-feeding organisms, suggesting that concentrations of small marine animals (plankton) became more abundant during the period. The animals from the Cambrian immediately before were mostly bottom scavengers or predators.
Organisms that stay in one place need some effective way to protect themselves from predators — they can’t swim away. Usually this consists of structural elements made from chemicals like calcium carbonate or silica, or for plants, lignin (bark). Tools of choice are the shell and nematocyst (stinging cells), the latter being popular among cnidarians (like coral) and the former among the rest. Some sessile animals, like the Pompeii worm that is found around volcanic vents on the seafloor, build a long tube around themselves as they grow and are capable of withdrawing themselves within it. Sponges are one of few sessile organisms with no overt defensive mechanisms, except for their low nutritional value and stomach-irritating spicules (spikes) made out of calcium carbonate or silica.