Literally, frog-mouse battle, from Greek βάτραχος (frog), μῦς (mouse), and μάχη (battle).
The source of the modern definition is Batrachomyomachia, a Greek comic epic about a one-day war fought over a misunderstanding; the author is currently uncertain but it is sometimes attributed to Homer, and is sometimes described as a parody of the Iliad.
Here's the short version:
A mouse meets the Frog King at the edge of a lake and is invited to his house. The Frog King starts swimming across the lake with the mouse seated on his back, but is confronted by a frightening water-snake. The frog dives, forgetting about the mouse on his back, who then drowns. Another mouse witnesses this from the shore, thinks the drowning was deliberate, and runs to tell the other mice. The mice declare ware on the treacherous frog king. Just before total mouse victory, the gods get involved and use crabs to defend the remaining frogs. The mice retreat and the war ends.
English Landscaper Henry Bright painted the battle.
"The petty forces of this or that little bit of a republic are for ever waging a kind of batrachomyomachia with those of some equally puny rival." - from "Lima, or Sketches of the Capital of Peru" by Manuel Fuentes, 1866.