It is neither the date of collection (in most cases) nor the date of edit/verification.
Because it is practically impossible to count all the people on a single day, the enumeration date is used as an "as of" date, meaning no matter when the census data is recorded, it was supposed to be "as of" a certain date. For example, the 1920 U.S. Census enumeration date was January 1, 1920 meaning the information on the forms was theoretically as of that date; however, there is no certainty that every census taker adhered to this rule.