BrandMentions' Performance score shows how important a mention is. It is calculated based on the number of total shares and the page's domain influence.
Domain Influence is a score that gives you an overall information about the authority of a domain.
Performance score mixes the domain influence score with social shares metrics. The score ranges from 0 to 100. Therefore a mention is performant as long as it comes from a high influence domain but also has a social engagement (high number of shares/likes/comments, etc). You can have mentions coming from sites with a high domain influence but with little engagement, and therefore the performance of that mention won't be high.