What does this Mizmor discuss?
Rashi: It is when they descended to Galus [Bavel], and Nebuchadnetzar asked [the Leviyim] to sing for him like they used to sing on the Duchan (in the Mikdash). Radak (6) - until verse 6 speaks on behalf of the Leviyim. After that, the author speaks.
Malbim: It is about the first year that Koresh conquered Bavel.
Why does it mention the rivers of Bavel?
Radak: There they sat isolated and devastated, and cried over memory of Tziyon.
Malbim: We did not cry over Tziyon due to loss of physical goods - wealth, acquisitions, fields and vineyards. We sat also on the rivers of Bavel. Also there we had an inheritance of fields and vineyards - "Benu Vatim v'Shevu v'Nit'u Ganos v'Ichlu Es Piryan" (Yirmeyah 29:5). Rather, we cried over the Kedushah of Tziyon - there was the Beis ha'Mikdash, Avodah and Shechinah, the spiritual happiness that we lost.