An impact narrative is a compelling statement that spells out a researcher's contributions to knowledge, health, environment, economy, society or culture.
In some cases, narratives may include publications, metrics, grants and awards, but these should fit coherently within the concise statement, precluding long lists of outputs or accomplishments. The focus is instead on capturing and evidencing the changes that might have occurred as a result of your research output being adopted, adapted or built upon. Impact narratives provide an opportunity to outline the background that shaped your research, the significance of your contributions, and the extent of stakeholder benefits.
In many instances, an impact narrative will be tailored to demonstrate relevance of your work to a specific project such as grant application. In these cases, ensure that you check which metrics are allowable for inclusion.
The NIH (National Institutes for Health) has for many years required grant applicants to include a "biosketch" to demonstrate the magnitude and significance of scientific advances associated with their discoveries, and the specific role they played in those findings. See https://grants.nih.gov/grants/forms/biosketch.htm
NHMRC also assesses research impact in many of its grant application processes, and publishes impact case studies which demonstrate strong impact narratives. See https://www.nhmrc.gov.au/about-us/resources/impact-case-studies
The ARC Data Portal contains both engagement narratives and impact studies that received a 'high' rating in the Engagement and Impact Assessment 2018, and could be used as best practice examples of impact narratives in a range of disciplines. For example, the impact studies can be searched by Field of Research code (e.g. "18" for Law and Legal Studies).
See https://www.arc.gov.au/engagement-and-impact-assessment