Examples of phenomena it explains include: how roots grow around obstacles, how trees seek out holes in the canopy, how brains learn, how the immune systems adapts to pathogens. It helps to explain how organisms develop diverse phenotypes from similar phenotypes - i.e. developmental plasticity.
Since DNA copying fidelity is often high - and organism lifespans are often short - there typically isn't much DNA-evolution involved in evolutionary ontogeny. Instead, position, chemical gradients and other factors evolve during development.
Developmental biology has paid little attention to evolutionary theory to date. However, an evolutionary approach to development seems likely to bring similar benefits to those that it has brought elsewhere in the life sciences.
The field is sometimes called "Evo-Devo" though typically then the only evolution involved is the historical kind.