It throttles the CPU way down, keeps the screen off, doesn't spin up hard drives- in practice it takes almost no battery. Even so, you can turn it off, trivially.

I don't know if you think that everyone urging you to upgrade is lying to you or if you're just being obstinate. It's OK if you don't want to upgrade to Mountain Lion but stop complaining about problems that have been solved.

I haven't noticed any meaningful drop in battery from this feature. Also, if you have Power Nap turned on while on battery power, and the battery level reaches 30 percent of capacity, Power Nap will be suspended.

However, Power Nap only works on recent Apple notebooks with flash storage and cool microprocessors (like your MacBook Air).

http://arstechnica.com/apple/2012/07/os-x-10-8/18/#power-man...

http://www.macworld.com/article/1167970/up_close_with_mounta...

If you're really worried you can disable it in System Preferences, but the latest Intel processors have new "active idle" states specifically for this kind of thing.

I'm guessing that by "connected to a power source" they don't mean the battery.