How does social media marketing influence people?

It's not the medium. It's the message, and a number of human dynamics that enable "influence" of one person over another to take place. 

"Influence: The Psychology of Persuasion". They are:ReciprocationSocial ProofCommitment and ConsistencyLiking Authority ScarcitySocial media can be a powerful conduit on which to execute numerous influence strategies, but the human dynamics that enable these influence strategies have very little to do with the communication channel itself.

Social Media Marketing (SMM) takes advantage of the human need for community and social interaction. By nature, we like to talk about, endorse or criticise the businesses, products and services that we use, want or like. Add to this the value our friends and acquaintances place on our opinions, social influence in commerce becomes a very powerful marketing tool. It goes beyond the commerce to analyse and manage image or reputation, build goodwill or likeability - which eventually translates into referral or walk-ins later on, and many such soft factors in business.