Wikipedia: Dog days

The term "Dog Days" was used by the Greeks (see, e.g., Aristotle's Physics, 199a2), as well as the ancient Romans (who called these days caniculares dies (days of the dogs)) after Sirius (the "Dog Star"), the brightest star in the heavens besides the Sun.

Popularly believed to be an evil time "when the seas boiled, wine turned sour, dogs grew mad, and all creatures became languid, causing to man burning fevers, hysterics, and phrensies" - Brady's Clavis Calendarium, 1813.

The Dog Days originally were the days when Sirius, the Dog Star, rose just before or at the same time as sunrise (heliacal rising), which is no longer true owing to precession of the equinoxes. The ancients sacrificed a brown dog at the beginning of the Dog Days to appease the rage of Sirius, believing that that star was the cause of the hot, sultry weather.

The Old Farmer's Almanac lists the traditional timing of the Dog Days as the 40 days beginning July 3 and ending August 11, coinciding with the ancient heliacal (at sunrise) rising of the Dog Star, Sirius.
According to The Book of Common Prayer (1552), the "Dog Daies" begin on July 6 and end on August 17.