Metabolism is a complicated chemical process, so we tend to think of it simply as something that influences how easily our bodies gain or lose weight. That's where calories come in as they measure how much energy (fuel) a particular food provides to our body.
Just as a car will store petrol in the tank until it is needed to fuel the engine, the body stores calories - primarily as fat. If you overfill the tank, it spills over. Likewise, if you eat too many calories they "spill over" in the form of excess fat on the body. Where this fat goes is dependant on the individual. For women it can be hips, thighs, bums or tums. For men it is more often on the belly and face. Men generally have a higher metabolism than women.
The number of calories a person burns in a day is affected by how much that person exercises, the amount of fat and muscle in his or her body, and the person's basal metabolic rate (look up BMR). Your BMR is usually inherited and depends on your body composition, but you can effect change by exercise and healthy eating. People with more muscle and less fat have higher BMRs.
Low calorie diets can slow down metabolism, hence a healthy balance combined with exercise is recommended over a fair period of time to allow your body, and metabolism to get used to the idea of regulated supply & demand. Generally though, whatever your metabolism rate and dietary intake, the usual suspect for not losing excess weight is a lack of exercise or working out (weights etc), which can increase metabolism.