What are the best exercises to firm up the back of my upper arms that jiggle??

YOu can't spot reduce, so to help get rid of the fat in the body you have to do cardio.
There are excercises that help tone the area, but again, cardio must be done as well.
Ticep kickbak, overheadpress, skullcrushers,tircicp dips and tricep pushups are the most common things I can think of to really help target that muscle group.

Tricep pushups are done by lying on one side of the body , the arm closest to the floor, should wrap to grab your waist, the arm on top should haveyour palm "starfished"- all fingers spread apart placed on the floor right around the nipple line, then push up with that hand and lower slowly with the same had. Your legs shold not move from the floor during the move at all.
These can also be done if you have a step 12-14 inches high, place both hands on the step, elbows tight to the waist, knees to the floor giving you enough room to have your upper torso come close to the top of the step, then slowly lower, and push back up.
You can also get in a downward dog pose, then carefully lower to plank, then "elbow shave" (arms should be straight and close to the body and lower your body to the ground, coming into cobra pose, then repeat.)

I'm not sure what to call them ... I lay on my back with my knees up, with a toooo heavy barbell just a few inches away from the top of my head. Then reach back and pretend to lift the barbell. I grip under. I have to focus on my triceps because it's also good for upper abs. At least I can always feel them there too.
You could use the bottom of your sofa too.

I am new here but I really noticed my arms yesterday and was shocked...My first reaction was to cry, where did all that chicken flabby fat come from omg. Help and more help please.....

Patty7, I'm in the same boat. I have HUGE, GINORMOUS, flabby arms. I, too, am looking for help firming them up. Do I need to buy weights? How heavy should they be? Can I get them at my local Wal-mart/K-mart or do I need to take a trip to some sort of fitness store?

You can get hand weights at WalMart.

You will need to get weights to work the tricep muscle and weights can be found at Wallyworld for about $1 per pound. If you have a Play It Again Sports nearby, you can get used dumbbells for much less than $1 per pound.
So far as poundage goes, whatever weight you can do the movement with GOOD form without the weight being too heavy and don't cheat with a weight that is too light. I began with 3# and currently go up to 20# for my own routines. If you are new to weight training, I suggest 3, 5 and 8 pounds to start and as the muscle gets stronger and the weight feels lighter you will need to increase the poundage to make the muscle respond.

Tricep dips are perfect for toning up muscles in that area. Just search for that in google if you need a picture. Basically you sit on a bench or *sturdy* chair and then lower yourself down and back up.

All of the exercises previously noted will do wonders for you. I also recommend basic push-ups for overall upper body and ab strength. If you cannot do regular push-ups, start with doing push ups against the wall, then progress to push-ups with your knees on the ground, then finally to full-on push-ups. Push-ups do wonders for your arms, chest and abs.

Here are some examples of the tricep exercises

FINALLY I have some help with this! I've been exercising with cardio and weights, and my arms are getting really toned up... except for the flabby backs. I can't wait to start these exercises!

Mercy, I thought I was the only girl on the face of the earth who couldn't go sleeveless!!!! These exercises oughta help!

In case any of you get discouraged about not losing the giggly arms if you do these exercise, it is a definite MUST to have a good healthy eating plan or a clean diet as I like to call it, AND incorporate intense cardio to lose weight. Once the fat on top of the muscle goes away, you'll have nice toned arms