A velvet hammer is a marketing tactic; a scheme wherein your customer gets his customers or suppliers to pay for the product you are selling.
Imagine that you are a publisher of specialty magazines. Your customers are large building contractors. You are attempting to sell a new prospect, United Residential Homes, the idea that they should publish a monthly magazine about their company. This will not cost United anything. You will sell advertising in the magazine to United's suppliers: plumbers, electricians, painters, interior decorators, etc. However, you expect United to call these suppliers and lean on them to cooperate with your salesmen. This is called the "velvet hammer."