The Ancient Egyptians, Greeks, and other nearby cultures noticed the star Sirius of the constellation Canis Major (Greater Dog) appeared at their height during the hottest time of the year. The corelation between the astronomy and climate that the name Sirius even comes from the Greek meaning "scorcher." (While some may have dreaded the rise of Sirius because of the heat, the Ancient Egyptians eagerly anticipated the rise of the "watch dog" as it gave advanced notice of the yearly flooding of the Nile River).
The Dog Days today though are not the same as they were in the past though. Sarah Jane of National Geographic's My Wonderful has written "These days, Sirius rises with the Sun earlier during the summer months, due to a phenomenon called axial precession, which means that the Earth's axis of rotation shifts slightly over time." Axial precession affects the way the Earth tilts and therefore impacts when the Sirus rises and meets its maximum height. The 1559 Anglican Book of Common Prayer has the Dog Days starting on July 7 and ending on August 18. The Farmer's Almanac (2010) has the Dog Days between July 3 and August 11. Going back in time the Ancients experienced the Dog Days between late July and very late August.