The ancient Romans believed this bright star -- the brightest in the night sky -- was the cause of the season's high temperatures. Good guess, but wrong. Still, that's where we get the phrase "the dog days of summer."
In ancient Rome, the dog days were said to linger from July 24 to August 24, when the sun and Sirius rose and set in tandem. Today, the constellations are not in exactly the same place in the sky, due to the "precession of the equinoxes," so the timing has changed a little.
Growing up, I always assumed "dog days" were days when it was so hot that all dogs could do was lie around in the shade, trying to stay cool. Cats, too.