When the dog star Sirius rises with the morning sun, it marks the most uncomfortable time of summer.
The “dog days of summer” are traditionally some of the hottest most uncomfortable days of the year (running more or less from July 3 through August 11 in the northern hemisphere). The ancient Greeks associated this time with heat, drought, sudden thunderstorms, lethargy, fever, and bad luck.
They are called the “dog days” because it’s at this time the star Sirius (which is actually a binary two star system) begins to rise at dawn along with the sun. Sirius is known as the “dog star” and is a part of the constellation of Canis Majoris (Latin “Greater Dog)”, all of which puts the “dog” in the “dog days”. It was thought that the morning appearance of Sirius, which is otherwise the brightest star in the night sky, added extra heat to the days making them more uncomfortable.
Potential spoiler: Sirius being the dog star is also the hidden-in-plain-sight reference with the character Sirius Black in Harry Potter, whose animagus ability is to turn himself into a dog.