It is often thought that exercising at lower intensities such as walking, burns more fat than at higher intensities (e.g. running). The science behind it is true in so much as when we work at lower intensities we require less 'quick release' energy (in the form of carbohydrates) therefore our body utilises a higher fat-to-carbohydrate ratio.
In order to lose weight you need to burn more calories than your body consumes and uses every day. In other words you need to be in calorie deficit. When we walk instead of run for instance, we burn fewer calories in the same amount of time the exercise is performed. More precisely, if you burn 250 calories everyday from a short fast jog, you'll see a bigger difference in weight and fat loss than if you walked everyday for the same amount of time. There is a higher percentage of fat being used during the walk but overall a lower total of fat is lost.
Intensity is the key here. The more effort you put in, the higher your heart rate therefore the more calories you burn. If you go to the gym and spend an hour chatting to your mate on the cross-trainer next to you, you're not working hard enough!