The term 'BAKER's Neighbor in 'Into the Woods'' is referring to the character of the WITCH, who is the neighbor of the BAKER and his wife in the musical. The WITCH is a powerful figure in the story, as she is the one who sets the plot in motion by placing a curse on the BAKER's family. She also serves as a mentor to the BAKER and his wife, helping them to understand the consequences of their actions and guiding them on their journey.