means The layer of vegetation—shrubs, saplings, and young trees—growing beneath the main forest canopy but above the ground-hugging plants.

from A transparent compound: "under" plus "story" in its architectural sense—a level or floor of a building, the same "story" you climb in a multi-story house. (That "story," meaning a horizontal layer, is likely the same word as the narrative "story," possibly from medieval builders decorating each floor with painted tiers of pictures, though the link is debated.) So the understory is literally the forest's lower floor, a botanist's borrowing of building-talk that took root in the 19th century.