Another good point to note is there are some exercises, when used with bad form can most definitely cause wrist pain, such as the Tricep Press for example. I know I had this issue when I first started using the TRX. The problem was I was bending my wrists, moreso than my elbows without thinking about it. After starting to experience some wrist pain, I watched a few videos of it being performed, and corrected my form, and haven't had a problem since... 
Some terminology that Fraser just thrown out there that you may not be familiar with that I thought I'd clear up for you are:
Supine / Supination - Backside down, frontside up. The "supine position" is laying on your back, with your anterior or front side of your body upward.
Prone / Pronation - Just the opposite of supination; backside down, fronside up. If you were laying in a "prone position", you'd be laying on your belly.
In context to this, what Fraser is basically saying is work with your hands/wrists both supinated and pronated meaning do a set of say bicep curls, first with the palms of your hands face up (supinated) like you traditionally would. Next to a set with your palms face down (pronated), so you are building up more of your forearms, dropping the focus on your biceps. This will also build up strength in your wrists (carpals).
Switch off from one to the other in multiple sets. Maybe like 2 or 3 sets each supinated, then pronated would be appropriate, but that is entirely up to you.
Lastly, the Extensor muscle said simply, is just the top side of your forearms.
And Fraser - Not to be sarcastic or anything, but I don't think it's humanly possible for your triceps to be any other way but pronated while exercising. If you twist your arms inward towards your chest they can be supinated, but if you tried working out with your arms like that you'd be sure to dislocate both the ulna and radius from their ligaments... 
Geeze Fraser, glad there is somebody here to break it down for them! LOL 