The psychologist Robert Cialdini made the term widely known in his 1984 book Influence, as one of six principles of persuasion. It works because judging every choice from scratch is hard, so people look for evidence that others like them have made it and been glad they did.
The strongest social proof is specific and comes from people the audience identifies with: a named client describing a real result counts for more than a vague five-star quote or a large follower count. It also has to be genuine. Invented reviews and bought followers break consumer protection rules in many countries, and once discovered, they destroy the trust they were meant to build.