"De" is the archaic form of the modern italian preposition "di" ("of").
The "de" form is still used in some central-italian dialects and is typically found in surnames of the same area. (mainly Lazio and Campania).
Etymologically, its roots can be tracked in Latin, where it was used in the "DE + ABLATIVE" constructions. It generally means "about, from or of". [A famous instance is the "De Bello Gallico" ("About the Gallic War") by Julius Cæsar.]
Thus, when used in surnames, it can roughly be translated as "Of/From the * family". In some case, it might indicate that a certain family is/was part of the aristocracy. (as stated above, especially in Central/Southern Italy).
Since you are talking about surnames, it is quite hard to get the meaning of them... but it is conceivable that e.g. "De Rossi" and "De Niro = De NEro" (De + Colour) are surnames linked with some kind of faction established during the late Middle-Ages.
About the "De + *s" question, as I said before, the original latin construction is "De + ABLATIVE". The -s is nothing more than the suffix of the ablative case. Indeed, the ablative ending of the adjective "sanct-us" ("holy, saint") in the plural form is "sanct-is"; so the meaning of the surname would be something like "[The family] Of the holy ones".