The Piazza Navona was built on the site of the Stadium of Domitian in the 1st century AD, and follows the form of the open space of the stadium. The ancient Romans went there to watch the "agones" (or "games"), and hence it was known as "Circus Agonalis" ("competition arena"). It is believed that over time the name changed from "avone" to "navone" and eventually to "navona".
It features important sculptural and creations: in the center stands the famous Fontana dei Quattro Fiumi or Fountain of the Four Rivers (1651) by Gian Lorenzo Bernini, topped by the Obelisk of Domitian, brought in pieces from the Circus of Maxentius.
Piazza Navona has two other fountains. At the southern end is the Fontana del Moro with a basin and four Tritons sculpted by Giacomo della Porta (1575) to which, in 1673, Bernini added a statue of a Moor, or a North African Muslim, wrestling with a dolphin. At the northern end is the Fountain of Neptune (1574) also created by Giacomo della Porta; the statue of Neptune, by Antonio Della Bitta, was added in 1878 to create a balance with La Fontana del Moro.
There's a myth that says the statue on the fountain with the upturned hand is reacting to the large facade of the church, as if frightened by it. In reality, the fountain was built long before the church, so there's no way the statues could have been sculpted as if they were scared of the church.
Read more about the Piazza Navona (link opens in a new window).