Which part of the back of the arm? The group is called triceps and there are 3 muscles there. You should be more specific on what you want like muscularity, definition or toning up. Depending on what you want and what kind of equipment you have access to, there are several excercises you can try and I know first hand works. I will suggest for excercises that do not need access to equipment and can do anywhere.
If you are able do close grip push-ups. If not start on the wall then down on the floor with your knees. Those will hit your bulk of your triceps.
You can also try dips supported on a bench edge of your couch. These will hit the muscles closer to your elbows.
You can also do Overhead extensions holding one dumbbell in each hand where you can do 12-15 reps for a set.
Do all 3 in a superset of 12-15 repetitions each, three times and you can see results in about two weeks.
This will also help tremendously. Cut back on carbs mostly white bread, white pasta, white rice, french fries and avoid fried foods. Instead eat wheat pasta, brown rice and baked foods. And do 20 minutes of cardio 3 times a week or more where your heart rate is at 120-140 BPMs for about 20 minutes. Yeah I think that might be overkill but if you want fast results you need to make changes if you have not already.
Hope that helps some. Let me know your progress! Go luck and have fun!
I would add to the above post to be sure and warm up before any type of workout. Having hurt both my shoulders lifting, I have learned my lesson and now take the extra 10 or 15 minutes before I get going. Dips can be especially hard on the shoulders.