This is a type of business association that is used in some civil law jurisdictions.
“Société” is used in the sense of a partnership. The anonymous part is that not all of the partners who have a stake in the partnership are publicly known. i believe that there had to be at least one partner who was publicly associated with the sociéte, but that silent investors could also be partners, without haveing their stake in the société a matter of public record.
I don’t know if this is still the case, what with all the concerns about money laundering and tax havens nowadays.
In short, your personal responsibility (your name) is not attached to your participation on the society. You have a stake (shares) and you are responsible or liable only up to the capital invested. Whatever evil happens to the company, you will not lose your shirt for it. Only the money you invested.
ETA: I think these are LLC (Limited Liability Company or Corporation) in the US, right?
In US usage, LLC & Corporation (usually written (“Company Name, Inc”) are legally distinct categories. Different rules apply to their formation, maintenance, ownership, and taxation. Corporations have been around in one form or another since the mid 1800s, whereas LLCs are a fairly modern (1960s?) invention.
But at a high level or viewed from a good distance, they are roughly equivelent to the Ltd, S.A. or GmbH organizations seen in Europe. Ownership is dispersed, managers need not be owners, owners need not be managers, and liablity for an organization’s losses does not extend to the owners beyond the potential loss of their investment.