"To win somebody over" is simply getting them to agree with you whether you are right or wrong. "As a salesman, I won a lot of people over and sold my products to them, even though some of them could not afford it." "A teacher who wins his students over is an effective teacher." "Adolf Hitler won many people over to his cause, even though his cause was desperately wrong!"

The question should be What does "to win somebody over " mean? It means to persuade somebody that you are right, or that a cause you like is worth supporting. 'My friend didn't want to vote for my brother, but eventually I won her over.'

It depends on the situation, but it basically means to get them on your side. You are in fact winning them over because you are doing something right.