The AA he's referring to is "apparent attenuation" - the percentage original gravity that was fermented out.

Your original gravity was 1.082 and your finishing gravity is 1.033. 33 is 39% of 82 (you remove the "1" in front of the decimal point because theoretically 1.000 is the lowest you can go) so your apparent attenuation is about 60%.

Thanks, Wutz! Based on the projected OG and FG from the kit paperwork, I was shooting for 75-80% AA. Is it always going to be around there that I want to shoot?

And what tangible effect will low AA result in? I'm guessing that the mouthfeel will be thicker than desired, the ABV will be lower than desired and the beer may be sweeter than intended. Is this correct, and what else might be affected.

The apparent attenuation is what you'll get out of the yeast if you provide an acceptable environment for them. If you get less than that, something went wrong. You just want to make sure you do everything you can to create a good fermentation environment for your yeast. Oxygenate/aerate, ferm at the right temp, make sure your wort is fermentable (moot point since you're an extract brewer), hydrate dry yeast/create starter for liquid yeast, pitch at the right rate, etc.

Personally, I think you will be just fine. Your bottling techique seems sound and should have dispersed the priming sugar properly (no stirring required or needed). As to a RIS finishing at 1.033, not the worst case scenario. I have an old ale that finished at 1..030 and it doesnt taste cloyingly sweet at all. If you gave your beer a good 2 wks or so, then your fermentation was probably mostly done providing you pitched enough healthy yeast and kept the temps fairly steady. I would be somewhat careful opening your first bottle though. Judge the carbonation level, and if it is a gusher, then put the rest of the bottles in a cold fridge to keep them from bursting. Now go brew another batch while you are waiting for this one!

Awesome! You get 50 points for telling me what I want to hear.

How did it go, donManguno? This is my first batch and I've got the same kit and similar numbers as you (1085 OG, 1032 FG); I took it off the cake early because I wanted to rack it onto some cherries and saw it suggested to move onto fruit before fermentation was complete. So, since it had already been going for 7 days in the primary, I racked it over to secondary last night and now activity appears to have stopped. I like the taste fine as is, but I want to avoid bottle bombs at all costs -- to the extent that I am considering omitting priming sugar during bottling. How did yours turn out?

If you are using dry yeast, make sure that in the future you rehydrate prior to pitching to get maximum healthy yeast over into the fermentor. If you were sprinkling in on top of your wort, you may not have started with the best numbers of yeast.

Speaking of rehydrating prior to pitching...how long should I wait after pitching before I pronounce my yeast DOA?

I rehydrated with half a cup of warm wort, and everything looked great. The yeast started foaming and doing their thing. I mistimed things, and had to hold them in the proofing mug for a couple hours while my wort cooled, but then I pitched, and all I get is a little foam. Granted, it's in a plastic bucket, so I can't see it directly (I think it's foam because the volume seems to have risen a half gallon on the side of the bucket). How long do I wait before I pitch new yeast?