The reason strength training helps you burn fat is because strength training stimulates muscle growth. When you have more muscle, you burn more fat calories.
Although aerobic exercise may be the most effective exercise for burning fat, when you do strength training the mitochondria in your muscle cells are stimulated and demand more nutrients in the cell to produce energy. Your cells then become more active, taking nutrients to other tissues and removing waste at a faster rate. Your muscles grow and continue this metabolic process after your exercise session.
Quotes from health professionals on this topic:
“Aerobic exercise is actually the most effective in losing weight, however, it’s not the best at burning fat and increasing lean mass (muscle)” – Noam Tamir, C.S.C.S., founder of TS Fitness.
“When you lift weights, you overload the muscle and it works to adapt to be able to lift more weight. The way the muscle adapts is by increasing something called myofibrillar size (the contractile units of the muscle), and while aerobic exercise can also [stimulate this process], this increase is not as great as it is with resistance exercise.” – Michaela Devries-Aboud, Ph.D., an exercise physiologist at McMaster University