The short answer
A brand lift study measures whether a marketing campaign changed how people perceive a brand (awareness, favorability, purchase intent), typically by surveying people who saw the campaign against a comparable group who didn't and comparing the difference. It answers a different question than clicks or engagement do. Not whether people interacted, but whether their opinion shifted.
Why this matters beyond standard engagement metrics
A campaign can earn strong engagement numbers while doing little to change how people think about a brand. The reverse happens too: real brand-perception change with modest engagement. A brand lift study is one of the only ways to measure the perception question directly, rather than inferring it from engagement as a rough proxy.
A realistic-scale version for a smaller business
A formal brand lift study is typically run by larger advertisers with the budget for structured survey research, but the idea scales down. A before-and-after survey of existing followers, or informally tracking sentiment in comments and DMs on either side of a campaign, captures a rough version of the same signal without the research apparatus.