The explanation is that your resting metabolism will increase: muscle tissue burns more calories than fat tissue. Here is a sample essay that includes the myth.
However, science says otherwise. An article in the October 2013 issue of the Berkeley Wellness Letter explains.
Some studies have found that resting metabolism stays at least modestly elevated for 12 hours or longer [after the strength training workout]...but average gym-goers don't work out long enough or hard enough to achieve any significant calorie-burning after-effect...So in that sample essay the claim is that the young woman gained 25 pounds of muscle. That would burn an extra 75 to 150 calories per day, which is insignificant compared to how many calories she burns through exercise (and also at most 4% of her daily calorie intake from food).
It's also true that strength training builds muscle, and that muscle burns more calories than body fat does...One pound of muscle typically burns 5 to 8 calories a day, though this depends on many variables, according to estimates by Robert Wolfe, Ph.D., professor of geriatrics at the University of Arkansas. In contrast, a pound of fat burns about 2 calories.
Losing one pound requires a deficit of about 3,500 calories. To lose fat, eat healthy and either eat fewer calories or exercise more (or both). A balanced exercise program includes both aerobic and strength training exercises.