From AMS Glossary
The period of greatest heat in summer.
Although the name is popularly supposed to have been derived from the period when dogs are especially liable to go mad, it is actually taken from Sirius, the Dog Star. In ancient Greece and Rome the heliacal rising of Sirius was associated with, and believed to cause, the hot, dry, sultry season of summer. The loss of human energy and the wilting of vegetation caused by this weather led to a belief in the baleful effect of Sirius on all human affairs. No formal meteorological or climatological definition exists. In the United States dog days are considered to persist for four to six weeks between mid-July and early September; in western Europe they last from about the third of July to the eleventh of August, and also are associated with the period of greatest frequency of thunder.