Understanding just how important dead trees are to a forest's overall ecosystem requires, firstly, understanding the greater life cycle of a forest. This life cycle is often referred to as 'succession' in which certain or multiple species change over a period of time in one region. Succession can be either primary or secondary with primary succession occuring when a community of organisms takes over barren land whereas secondary succession occurs when a community of organisms takes over a section of bothered or disturbed land, often due to events like wildfires or floods.
Another way to think about succession is by comparing it to a human's life cycle. When forests begin to grow, the first plants are only small shrubs and grasses and when we begin to grow, we start as babies and grow into toddlers. Then, soft trees begin to grow in the forest; we transition from toddlers into children and teenagers. Lastly, as time moves on, these softwood trees make room for hardier trees and we, in our lifecycle, become adults and elders.
However, rather than the whole forest dying at once at the end of its life cycle, singular dead trees simply collapse and go on to exist as an entirely new "species" in the forest, providing valuable services to the trees growing around it. While this "species" can still be referred to as a dead tree, the typical term is deadwood. For something to be classified as a deadwood, it has to be a woody, non-living mass found in a forest with the most common types being fallen logs, snags (standing dead trees), large branches, or very large roots. They also have to be in the process of decomposing, doing so thanks to decomposer and saproxylic species, which are dependent on decaying deadwood.
In historical silviculture (forest management) practices, deadwood was typically removed. Now as the science behind deadwood increases, better forest management practices can be implemented that work to preserve this deadwood and in turn, the biodiversity of species that rely on deadwood, especially saproxylic species, and every other benefit deadwood brings. In large forests, one such management technique is simply leaving the trees where they fall. This creates something known as 'pit and mound topography' where, over time, the dirt ball attached to the tree's roots leaves both a pit where it once was and a mound where it now is. One result of these pits are vernal (spring) pools that disappear in the summertime, yet provide a perfect site for laying eggs free from predators for small, forest dwelling amphibians.