Staff scientist is a broad category, so here’s a broad definition: these professionals (usually PHDs) serve as employees at companies and nonprofits to provide a scientific backbone to decisions made at the larger organization.
At an environmental protection nonprofit, for example, a staff scientist researches and reports on the problems that specific group wants to address. This puts hard evidence behind a mission. At a for-profit corporation, staff scientists may test products or study the broader industry and report back to boards.
Staff scientists can come from virtually any scientific background so long as their specialty is beneficial to the organization and they’re good enough communicators to translate complex findings into something that relates to an organization’s bottom line.