AVR = automatic voltage regulator, I would think. On most UPS that aren't really expensive, the implementation should be fairly cheap and not do that much—switch to a different voltage range if dipping below a certain threshold or going above another, or something like that.
If it's for a decent modern computer (power supply), I wouldn't worry too much about it. The APFC circuit that controls how and when power is drawn from the mains, input side filtering, and bulk capacitor(s) on the primary side should be able to handle most transient issues. I mean, even after that, there's PWM chopping up the input, going across a transformer, more rectification and filtering in the power supply, and additional regulators to bring down to something like CPU voltage, so mains power should be pretty far removed from what's happening inside the computer (you hope).
For most audio gear, you'd hope that the designs aren't so sensitive to power rail fluctuations and have the necessary filtering up front, but I guess if you really want, you can always baby them with external conditioners and so on. I mean, if operating conditions are really bad, as you've noted, they can help.