Ascriptive means the act of ascribing something based on particular qualities, usually beyond the person's control. In other words, in this usage, the act of determining status, rights and privileges in a society based upon things like, race, color, birth family, sex, hair color, etc.
In an ascriptive society, status is determined by a particular set of personal attributes that are generally not in the individual's control as opposed to an achievement based society where satus is determined by the past and expected future achievements of the individual.