What does Psalm 137:2 mean?

To "hang up" something is a common English expression of ending some effort or practice. An athlete who retires is said to "hang up" their cleats. Politicians defeated in an election may decide to "hang it up" and concede. The basic imagery is a person setting aside the tools for a job, recognizing that it's time to stop. In a parallel way, the captive Israelites (2 Chronicles 36:17–21) have no taste for singing. They hang their instruments on the tree branches, with no desire to play. This is not only from grief, but also because their captors are mocking their pain (Psalm 137:3).

In this case, the psalmist speaks of being near the waters of Babylon (Psalm 137:1). Babylon was known for its extensive river, canal, and irrigation network. The word naming the trees here is arābim', or arābāh, referring to a type of tree which preferred watery areas and had very dark wood. Scholars suggest this was the plant modern people call the Euphrates Poplar, which is a kind of willow tree (Isaiah 44:4; Leviticus 23:40).