The Collaborative International Dictionary
July \Ju*ly"\, n.; pl. Julies. [L. Julius; -- named from Caius Julius C[ae]sar, who was born in this month: cf. F. Juillet.] The seventh month of the year, containing thirty-one days.
Note: This month was called Quintilis, or the fifth month, according to the old Roman calendar, in which March was the first month of the year.
Wikipedia
In the ancient Roman calendar, Quintilis or Quinctilis was the month following Junius (June) and preceding Sextilis (August). Quintilis is Latin for "fifth": it was the fifth month (quintilis mensis) in the earliest calendar attributed to Romulus, which began with Martius (" Mars' month," March) and had 10 months. After the calendar reform that produced a 12-month year, Quintilis became the seventh month, but retained its name. In 45 BC, Julius Caesar instituted a new calendar (the Julian calendar) that corrected astronomical discrepancies in the old. After his death in 44 BC, the month of Quintilis, his birth month, was renamed Julius in his honor, hence July.
Quintilis was under the guardianship ( tutela) of the Romans' supreme deity Jupiter, with sacrifices made particularly to Neptune and Apollo. The importance of agricultural festivals directed at the harvest gradually lost their importance, and the month became dominated in urban Imperial Rome by the Ludi Apollinares, games ( ludi) in honor of Apollo. Ten days of games were celebrated in honor of Julius Caesar at the end of the month.