I used to be in the Industrial Hygiene business about 20 years ago, and what I find interesting is that no one can seem to decide on what the "A" stands for. Every time I see someone explain the acronym, it is different. Even the Certified Industrial Hygienists at my company (the people that are supposed to be the experts) couldn't seem to keep it straight. I always found it odd that they said it was "Absolute". That didn't seem right. "Air" would seem to make sense, except HEPA filtration is also applied to water too. Shane's "Arresting" isn't bad, but that's the first time I've noticed that variant.
After a Google search for "High Efficiency Particulate", it doesn't help much. Air was the most common, with Arresting coming in close, but I even found "Absorbing". What's a little more telling, though, is that quite a few references don't use anything for the "A" at all, and it is just High Efficiency Particulate filter.
ACGIH (American Conference of Industrial Hygienists, but formerly American Conference of Government Industrial Hygienists) --see, they can't even keep the acronym for their own name consistent--use "Air", but I suspect this has changed over the recent years. All of our CIH's were members of ACGIH, so if there was agreement on it back then, it would have been used. Maybe back then the agreement was "Absolute" but has been changed. It would be interesting to find out what the original usage of the acronym was.
Edit: After a little more digging, I am starting to think that the original word was in fact the "Absolute" that our CIH's were using 20 years ago. That makes sense because the "C" in CIH is the equivalent of being a PE in engineering, and they were very careful with how a report was written. It also makes sense, considering the acronym was originally developed by the DOD during the Manhattan Project, where the intent was to remove radioactive particles at the "absolute" level.