The term has its origins from ancient cultures interpretation of astronomy. Around this time Sirius aka the dog star rises around the same time as the sun. The star is the brightest star besides the sun. Egyptian culture noticed Sirius rose right before the Nile flooded and served as a watchdog or reminder for Egyptians to prepare and celebrate the return of rains. Romans believed the star caused the warm weather. They feared these days due to the heat and what they believed were a related increase in animal attacks.
Today the term dog days makes one think of dogs being lazy in the heat. However, as remarked in Romeo and Juliet, the heat can cause one to be more prone to violence. Hot summers are the stereotypical time for riots and short tempers.