Biomass is material derived from living things, such as wood, grasses or manure. Sometimes it is a byproduct of some other process, but it can also be produced intentionally, such as the growing of corn for producing bioethanol. Biomass can be used to generate electricity.
The simplest way to generate electricity from biomass is to burn it. Just like burning coal, oil or gas, the heat generated turns water into high-pressure steam that is used to drive a turbine that generates electricity. Biomass can be burnt on its own or along with regular fossil fuels.
Biomass can be heated in a controlled oxygen environment, so it does not burn, but instead produces a mixture of gases including methane, hydrogen and carbon monoxide. These gases can drive electricity-generating turbines or be burnt to generate steam, which in turn drives the turbines.
Allowing microorganisms to break down the biomass in oxygen-free conditions can produce ethanol and methane. These can then be burnt to drive steam powered turbines.
For the most part, theses methods all involve burning biomass or burning products derived from the biomass. This principle is the same as how electricity is generated from fossil fuels.