OK, I got smuhrt and decided to Google it.
Apparently, it's a pretty meaningless and in a lot of ways misleading claim.
The standard drycleaning solvent, Perc, is that everyone is worried about.
But, because Perc is a carbon-based compound, it is considered chemically "organic."
So, dry cleaners who use Perc can claim that they are "organic" dry cleaners and separate the hippy idiots from their cash.