Strictly speaking, "biological energy" ought to refer to the chemical potentials produced and consumed by the myriad and interwoven reactions that take place within the compartments of living matter as it... well, lives! But these processes are perhaps better known, collectively, as metabolism.
We use the phrase "biological energy" as a convention to refer to a specific social and technological endeavor: to use the metabolic capacities of organisms to convert some combination of light, biomass, organic compounds, gases and water into useful chemical-bond energy; i.e. storable, transportable, energy yielding molecules as well as industrially useful materials. Examples include hydrogen, methane, alcohols, ammonia and bioplastics.
The purpose of designing and developing biological energy systems is to reduce the emissions of greenhouse gases and provide environmentally friendly alternatives to some industrial processes. Biological energy is sustainable technology.
The development and implementation of these processes to the point of economically competitive technologies will require the coordinated efforts of science, engineering, business and government policy.