This is the phrase that best captures, I think, this peculiar form of company rather unique to France. Widely popular as a form of buying real estate among families wishing to avoid excessive inheritance taxes in the 1960s, it is less popular now because of changes in the inheritance laws. Typically a well-endowed family could establish an SCI to buy or construct a new home and provide in the articles of incorporation a means for succession that effectively side-stepped conventional inheritance. (Not surprisingly, there have been a lot of scandals related to the abuse of this legal device.) Nevertheless, it is not limited to use by private individuals as a means of holding "private property":it is also used by large corporations as a means to develop condominiums or individual large estates. This translation Real Estate Investment Company is inclusive enough to permit all these usages. The key point is that all sociétés are civiles, but a company designated Société civile immobilière is contrasted with sociétés commerciales in particular.

I have done quite a lot of in-depth research on this in France,preparatory to buying real estate here, and have also consulted with CPAs concerning its desirabiilty. See the following references:
Cornu, Vocabulaire judiciaire
Thierry Andrier, Guide pratique des sociétés civiles immpbilières (Paris: Litec, 1999)
Guide juridique à la Société Civile immobilière (I cannot put my hands on this one at the moment, but it is in one of those popular legal series)

Hope this helps!