Strength training is very important when you're trying to lose weight--even if you're not interested in becoming Mr. or Ms. Universe. Strength training not only tones your body, it boosts your metabolism so you will burn more calories at rest.
Here's how: When you exercise regularly, you build up the proportion of muscle in the body compared with fat. Unfortunately, lean body mass decreases with age in everyone, regardless of how fit you are. If you don't do anything to preserve your muscle, it will be replaced by fat. If that's not motivation for strength training, what is? But remember that you don't have to spend all day lifting weights. One or two sets of 10 to 12 repetitions of moderate weight will tone your muscles and improve your posture and overall physique.
As you become more experienced, or if you are strength training as part of a cross-training program to keep you fit for other sports, strive for balance between opposing muscle groups. That means you should lift similar amounts of weight for opposing muscle groups, such as the biceps and triceps, or the quads and hamstrings. Some groups may be stronger than others, and that's ok. For example, if you are a runner, the weights you are lifting with your hamstrings may feel easy. Because your hamstrings get plenty of exercise from running, it is better to lift less with them than to lift more with your quads to achieve balanced muscle strength.
Include opposing muscle groups in your strength training sessions. In half an hour, you can fit in 2-3 sets of 10-15 repetitions for a few key muscle group pairs:

• hamstrings/quadriceps
• adductor/abductor muscles (inner and outer hip)
• calf muscles
• biceps/triceps
• shoulders