The Extract Field from Object integration by Clay allows users to quickly and easily extract various information fields from a data array or object. It transforms complex object structures into a cleaner, readable list. The interactive demonstration in the video highlights the extraction of job titles from a jobs object, delivering them in a neat comma-separated text format. This list can then be exported or mapped onto a table to further streamline workflows. Whether dealing with data science roles or risk management positions, this integration creates a straightforward way to distill object data.