This kind of intersects with some research I'm doing so I'll take a stab at answering.
Something psychologists, sociologists, and advertisers have known for a long time is that your behavior is heavily influenced by the people you interact with. If your friends all started getting in to a new TV show, you'd probably start getting into it too. If your friends are mostly Republicans, you will be more likely to be a Republican. This is kind of obvious, but it extends towards more commoditized things as well. If your friends all use iPhones or have Beats, for example, when it comes time to buy a new smartphone or headphones, you are more likely to buy an iPhone or Beats.
Within the past 10-15 years, two very important things happened. First, social networks became almost ubiquitously popular among many demographics. These networks are able to collect large amounts of data on their users' behaviors and preferences. This allows for personalized advertisement, which uses this data to determine the value of showing a specific advertisement to a person; this is the second big thing.
An innovative idea came in extending the concept of friends influencing purchases to social networking: when advertising to members of a social network, you should not only consider the value of a sale to an ad target, but also the expected value of the sales gained from that member influencing other members [0]. This was further formalized in 2003 by presenting the problem as follows: create a graph with vertices representing social network members and edges representing probabilities of one member influencing another to buy a product via influence propagation [1]. If you are only allowed to target k members of the network to influence, how do you pick the k members that will maximize influence propagation? Although this is an NP-complete problem, good ways to approximate might be to look at max degree vertices, or to generalize, vertices with neighbors (with neighbors with neighbors with neighbors... etc.) with lots of neighbors.
So this gets back to why someone can be paid to be a social influencer. First, a social influencer is a real person with "real" connections to the people that are connected with them via a social network, so they are likely to influence those they come into contact with to buy new products. Secondly, because having both quantity and quality of connections within a social network enhances the number of people you can reach, you want to look at people with high engagement and high number of followers. These people are able to influence a lot of people to buy products, so they get paid to do so.
[0] http://homes.cs.washington.edu/~pedrod/papers/kdd01a.pdf
[1] http://www.cs.cornell.edu/home/kleinber/kdd03-inf.pdf