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."
The Velvet Hammer is a women leader or professor who can manage with grace and eloquence and still get things done. She is very tough on her underlings, but fair and brilliant. She is also very beautiful and probably will save/rule the world one day.
Oh man, did you see the requirements for that final paper she has us doing?? That woman is the Velvet Hammer!