Definitions of woody:

• adjective:   made of or containing or resembling wood

  Example: "Woody plants"

• adjective:   made hard like wood as the result of the deposition of lignin in the cell walls
• adjective:   abounding in trees

  Example: "A woody area near the highway"

• name:  A surname (common: 1 in 14285 families; popularity rank in the U.S.: #1664)