Most forms of exercise will help increase your ratio of lean muscle to fat. But unfortunately, it does little to target your particular problem area that you are discussing here, the backs of your arms.
To do this, you need to do some exercises to firm up your triceps. Adding some tone to this area will definitely affect the jiggle factor. So here are a couple of exercises that can help:
Bench dips
Sit on the edge of your bed or a sturdy chair with your palms planted on each side of your hips and your fingers hanging over the edge. Walk your feet out a little so that your hips are off the bed; your butt should just clear the edge as you use your arms to lower yourself.
Keeping your knees bent, lower yourself until your elbows are at 90 degrees and your upper arms are parallel to the floor. Use your arms to raise yourself up and continue to raise and lower 12-15 times. Do two to three sets. As this becomes easier, do the exercise with your legs straight.
Triceps kickbacks
Use a small dumbbell or some substitute (such as a can of tomatoes or a bottle of ammonia). Bend over at the waist, resting your hand on a chair, so that your back is flat. Grasping the weight in the other hand, bring your bent elbow up to your side and keep it there. This is the start position.
Now, keeping your elbow pinned to your side, extend your arm back until the elbow is straight, then lower and repeat 12-15 times. Do two to three sets. As this gets to be too easy, increase the weight.
Resistance training (weights or straps) needs to be 'volume progressive' in order to replace lost muscle tissue, or build up muscle.
So, use triceps exercises with progressive resistance in order to build up muscle, in your quest to "tone up" arm flab.