From the book: http://www.datascienceassn.org/sites/default/files/Building Data Science Teams.pdf
A data-driven organization acquires, processes, and leverages data in a timely fashion to create efficiencies, iterate on and develop new products, and navigate the competitive landscape.
Author wrote also:
There are many ways to assess whether an organization is data driven. Some like to talk about how much data they generate. Others like to talk about the sophistication of data they use, or the process of internalizing data. I prefer to start by highlighting organizations that use data effectively.
See also: altexsoft.com blog post on datascience: how-to-structure-data-science-team-key-models-and-roles