Do you have a problem with excess fat hanging off of the bottom of your arm? If so, don't worry! This is a very common problem and can be addressed with proper exercise.
The first thing you have to know is that spot reduction, the idea that doing exercises for the muscles under the arm flab will get rid of the arm flab, is not true. Your body chooses what fat deposits to take energy from in a predetermined pattern, so you cannot "make" it take the underarm flab first. Therefore, you have to burn far from your body in general in order to make it take some from your underarms.
Still, I do recommend that you do exercises for your triceps, which is the muscle that underlies your underarm. If you tone your triceps it will cause the skin of the arm to hang higher, which will improve the appearance of the entire arm. Try doing 4 sets of 10 reps of tricep press downs followed by 4 sets of 10 reps of close grip bench press next time you are in the gym. Don't use too much weight when doing these movements, and really focus on feeling your triceps working. You will see an improvement in the tone of your arm quickly if you do these movements on a regular basis.
And, of course, you have to burn some calories in order to get rid of that fat. Try inserting workouts into your normal daily routine. For example, if you are going out with co-workers for lunch try to walk to the restaurant instead of drive. It may not seem like much, but if you do this over time the fat losses start to really add up. As far as work in the gym goes, try to do 3 moderate intensity cardio sessions per week. You can do the stationary bike, the elliptical, the treadmill... just about anything that gets your heart rate up and makes you sweat.
Put these strategies into action and I am sure you will have the toned, sexy arms of a fitness model in no time at all!