Ecological succession is the change of biological communities within a specific environment over time. It is a very simple idea, but it is also very important in order to understand how species interact with each other and how to keep ecosystems healthy. Succession is said to start from a point at which there is no or very little life in an area (primary or secondary succession), and continue through stages of development until it reaches a comparatively stable climax community.
Primary succession: The process of ecological succession originally starts in areas where there is no life. These days such places are rare, but may still be found on lava flows, sand bars and sand dunes, land that was previously covered by glaciers or ice sheets, etc. Newly formed bodies of water may also be considered sites of primary succession, even if there was technically life there before. Once conditions are right to support life, lichens and mosses appear on rock, grasses such as the Ammophila take root in sand, and algae and eel grass appear in bodies of water. In some cases the first species to move in are just bacteria (and in some environments, bacteria will also be the climax community).
Once the primary succession species (pioneer species) have moved into an area they slowly build up soil, increase nutrients, and otherwise prepare the site for other species. For example, Ammophila grasses grow exceptionally well on sand dunes, even rapidly shifting dunes. They are one of the very few types of plants that thrive in this environment. But their extensive root system and quick growth help stabilize the dunes, allowing species like Cottonwood to live on the stable sand. Once they die they provide nutrients for less hardy species, and slowly a true layer of topsoil can form. Eventually dunes will be changed into prairie or woodland.
Secondary succession: This type of succession occurs where vegetation is removed or destroyed, but soil remains. This is more common than primary succession, being caused by forest clearing, construction, farming, overgrazing, and other fun things humans do. It can also be caused by flooding, wildfires, introduction of new species, and drought.
In secondary succession the pioneer species are less likely to be algae and lichens and more likely to be graminoids and forbs, herbaceous plants that reproduce quickly and can take advantage of the nutrients already present in the soil. (On a personal sidenote, I live in an area where the soil is so poor, rocky, and windswept that the pioneer species are usually woody plants like pine and low shrubs; the characteristics of pioneer species depend greatly on the environment).
Seres: Once the process is set in motion, new communities follow each other in succession. These communities are called seres, or seral communities. Poor soil may be developed by hardy forbs and grasses ('weeds'), to be followed by small shrubs and trees; as the trees grow they provide shade that will discourage the growth of the original populations of grasses and forbs, but encourage the growth of shade-loving plants. The animal population will also change, perhaps moving from field mice and lizards to racoons and toads. As trees grow they will provide better cover for deer, wild pigs, and bear, but discourage buffalo and caribou. (But it could also go the other way; a healthy population of grasses and forbs may encourage grazing by ruminants, which prevent the growth of shrubs and trees that cannot recover from grazing as quickly as herbaceous plants can. In this case you would end up with meadows and prairies rather than woodlands.)
Climax community: The end point of ecological succession is the climax community. This is a community of species that live in a network of stable and sustainable relationships, which is generally unchanging, aside from seasonal differences and major environmental changes (such as wildfire, humans, and all those other factors listed above). But even long-term climax communities are temporary; even in a perfectly stable environment with no humans, invasive species, or disease, (and there are no environments like that), evolution and geological processes would still make slow changes in the species and their environment. Ecological succession is part of the natural state of an ecosystem, and minor adjustments are always occurring, even in the climax community.