We have used biomass energy for as long as there has been agriculture. Orchards, grain fields, etc. all produce excess wood, straw, etc. as byproducts: trees have finite lifespans, and for grains all we're interested in is the seeds, not the straw itself. So what have we done with these byproducts? Burn them, as fuel, to heat homes, etc. If anything, we use biomass energy less now than we once did, although when you buy almond firewood in California, you are buying trees from almond orchards that have reached the end of their lifespans.

Humans have used biomass for energy for a very long time, though most western countries do not use it currently as a main source of energy (~1%).

Biomass can be anything that was once living or a product of a living thing. This means a wood stove uses biomass. It could also be leaves, yard waste or animal droppings...yes, I mean poo.