Trust flow is a ranking signal calculated by Majestic, one of the major SEO tracking players. Particular attention is paid to the quality of the incoming and outgoing links. Majestic itself describes it as follows:

"A score based on quality, on a scale between 0-100. Majestic collated many trusted seed sites based on a manual review of the web. This process forms the foundation of Majestic Trust Flow. Sites closely linked to a trusted seed site can see higher scores, whereas sites that may have some questionable links would see a much lower score."

Not quite clear yet? It is further explained in the video.