A naumachia was the reenactment of a naval battle in a basin or on a lake, a popular albeit costly – and for the participants deadly – entertainment of the masses in ancient Rome. The term naumachia was also used for the location at which the games took place.
Our current read, Sand of the Arena, opens with an imaginative happening of the naumachia of Nero – “…he also exhibited a naval battle in salt water with sea monsters swimming about in it” according to Suetonius’ Life of Nero.
Smith's Dictionary via LacusCurtius has this to say (please note the many e-text links):
NAUMA‑CHIA was the name given to the representation of a sea-fight among the Romans, and also to the place where such engagements took place. These fights were sometimes exhibited in the Circus or Amphitheatre, sufficient water being introduced to float ships, but more generally in buildings especially devoted to this purpose. The first representation of a sea-fight on an extensive scale was exhibited by Julius Caesar, who caused a lake to be dug for the purpose in a part of the Campus Martius, called by Suetonius the “Lesser Codeta” (Dion Cass. XLIII.23; Suet. Jul. Caes. 39); this lake was afterwards filled up in the time of Augustus on the account of the malaria arising from the stagnant water in it (Dion Cass. XLV.17). Augustus also dug a lake (stagnum) near the Tiber for the same purpose, and planted around it a grove of trees (nemus) (Suet. Aug. 43; Tacit. Ann. XII.56, XIV.15). This naumachia was the first permanent one; it continued to be used after others had been made, and was subsequently called the “vetus naumachia” (Suet. Tit. 7; Dion Cass. LXVI.25; Ernesti, ad Suet. Tib. 72). Claudius exhibited a magnificent sea-fight on the lake Fucinus (Tacit. Ann. XII.56; Suet. Claud. 21
; Dion Cass. LX.33). Nero appears to have preferred the amphitheatre for these exhibitions. Domitian made a new naumachia, and erected a building of stone around it, in which the spectators might sit to see the engagement ( Dion Cass. LXVI.8; Suet. Dom. 4, 5). Representations of naumachiae are sometimes given on the coins of the emperors. (Scheffer, de Militia Navali, iii.2 pp189, 191).
The combatants in these sea-fights, called Naumachiarii (Suet. Claud. 21)
Known sponsors were Gaius Julius Caear and the emperors Augustus, (probably) Tiberius, Caligula, Claudius, Nero, Titus, Domitian, and Trajan. According to this Wikipedia article, Trajan's naumachia basin was discovered in the 18th century on the grounds of the Vatican City. It had bleachers and the surface was about one sixth the size of the Augustan naumachia. In the absence of any texts, it has to be assumed that it was only used at the time of Trajan. (see Naumachia Vaticana). Also, there, was a Naumachia Philippi (Philip the Arab), which may have been a restoration of the Naumachia Augusti.
Google Books has a related page from Daily Life in Ancient Rome: The People and the City at the Height of the Empire by Jerome Carcopino (revised 2003 with new material to the second edition 1968, Yale University Press, with an introduction & bibliographic essay by Mary Beard – neither of which, unfortunately, is online). Bryn Mawr Review.
An overview of naumachiae from Samuel Ball Platner (as completed and revised by Thomas Ashby): A Topographical Dictionary of Ancient Rome, London: Oxford University Press, 1929.
Augustus' Naumachia (Trastevere) here and here.
The etching on top of the post comes from the Naumachia page from Colosseum.net.
Modern naumachiae were performed in France in 1550 in Rouen for Henri II and Catherine de' Medici – view the illustration at the bottom of Fête triomphale et naumachie sur la Seine pour l’entrée royale d’Henri II à Rouen en 1550 – and in Milan in 1807 for Napoleon (figures, doesn't it?).
