Strength training helps you lose weight (and body fat) in a few different ways.

First, it helps you retain the muscle you have while eating a calorie deficit and losing weight.

Second, strength training has a much greater level of excess post-exercise oxygen consumption than aerobic exercise.  What does this mean?  When you finish a workout, your body needs to do a lot of work to replenish itself in order to bring itself back to a normal state (the way it was before you worked out).  This takes a lot of energy, and some studies have shown that it can boost your metabolism for up to 38 hours after you finish your workout.