The RACI framework is used to distribute roles when managing data quality, with Responsible referring to those who own execution steps within a project, Accountable for those who own the results of the project, Consulted for those who will be pulled in as needed, and Informed for those who need to be aware of what's happening. The text provides examples of how these roles can apply to data quality management across various teams such as data engineers, analytics engineers, data analysts, business stakeholders, and business system administrators/software engineers.