Every coin in your pocket carries the name of a Roman goddess. Money comes from Moneta, a title of Juno, because Rome's mint stood beside her temple.
The temple stood on the Arx, the northern peak of the Capitoline Hill. Livy says the dictator Lucius Furius Camillus vowed it to Juno Moneta in 345 BC, and it was dedicated a year later. Coins were first struck next to it, and the temple probably stored the metal. From 273 BC the silver mint and its workshops were attached to the building. Money was struck there for more than four centuries, until the emperor Domitian moved the mint near the Colosseum.
The goddess's title became the name of the place and then of its product. Latin moneta came to mean a mint, and then coined money. Old French made it monoie, modern French monnaie, and English had monie by the middle of the 13th century. At first it meant funds or means. The sense of coins and metal currency followed around 1300.
What Moneta meant is a harder question. The Romans connected it to monere, "to warn," which made Juno the goddess who gives warning. Cicero told of a voice from the temple during an earthquake, demanding the sacrifice of a pregnant sow. A better-known story involves Juno's sacred geese. In 390 BC, or 386 BC in some sources, they woke Marcus Manlius as Gauls climbed the Capitoline at night, after the dogs had failed to bark.
Most modern scholars reject that derivation. They note that Moneta was worshipped outside Rome and was probably identified with Juno only after her cult reached the city. Etymonline calls the warning etymology sensible but difficult. The link from the goddess's temple to money is solid, while the meaning of her title is not.
The same Latin word entered English twice. Long before the French borrowing, Old English took moneta as mynet, recorded in the 8th century. That became mint. Money and mint are doublets, two words from one source.