The metric HS Invocations represents the number of Hull Shader invocations. The Hull Shader is invoked once per patch.
The SimpleBezier11 sample from the Microsoft* DirectX* SDK is a good example to understand Hull Shaders. This sample renders a Mobius strip comprised of four patches with 64 control points per patch. Execution of this sample will result in an HS Invocations value of four.
The Hull Shader is not usually a performance bottleneck, but it can definitely cause performance issues further down the rendering pipeline. If the Hull Shader specifies large tessellation factors, or as the HS Invocations value increases, it will result in more work for the fixed function tessellator as well as an increased number of DS Invocations and GS Invocations.