Forest succession is the natural process by which the composition (kinds and amounts of the various small plant, shrub and tree species) of the vegetation in a forest ecosystem changes over time (years, decades, and, in some cases, centuries). The succession is unique for each different forest ecosystem.
In general (but remember that there can be significant differences in different ecosystems), starting from bare ground (such as may occur after a major, vegetation-clearing wildfire or other event) in a forest ecosystem, the initial vegetation components witin the first year or two are grasses, forbs, and smaller shrubs. Depending upon the availability of seed sources and the kind of ecosystem, tree species that require -- or at least can tolerate -- full sun, and perhaps drier conditions because of the lack of shade, begin to move in over a period of several years. Finally, the more shade tolerant species (and/or those which require more moist conditions) of shrubs and trees move in under the protection afforded by the canopy of the sun-loving species, and slowly become the dominant species in the stand, and will form the principle composition of the "mature" stand. Over periods of decades or longer, individuals in this stand will fall victim to insects and diease or other fates, and die to be replaced by yet other shade tolerant individuals that grow up into the canaopy. The specific species of plants and tree involved in all this will depend on the particular ecosystem.
Understanding forest succession for any ecosystem is of vital importance for the management of a forest area. By knowing the specific growing requirments and timing of the plant and tree vegetation that will naturally occur over the life cycle of a forest area that is being managed for the varied resources that are availabe on that area (e.g., wood, water, wildlife, recreation, minerals) professional foresters are able to optimize their production for the greatest benefit to society under principles of sustained yield and multiple use management. For example, contrary to what you may read or hear elsewhere, harvesting timber--when done in accordance with sound forest management practices which actually are based on an understanding of the particular ecosystem's natural succession--is not destructive to the forest environment, but in the long run will serve to enhance the environment and the utility of that forest stand for the production of goods and services for the benefit of society.