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This is a way to draw a mesh connected to a node hierarchy. Artists call the node hierarchy a skeleton or rig and the mesh for a skin. When the nodes move, the mesh will move with it and each vertex can be affected by more then one node. Skinning is only about drawing, it does not care about how the node hierarchy is animated. The process of connecting the mesh to the nodes is called binding and it sets up what nodes affect each vertex and by how much. This is normally done in art tools such as maya or max. If all vertices in a mesh is bound to the same node it's called a rigid bind else it's a smooth bind. The common limit of how many nodes can influence a vertex is four.

Each bones influence on a vertex is called it's blend weights.

Skinned Models in DirectX 11 with SlimDX and Assimp.Net - 2013
Over My Dead, Polygonal Body - 1999
Skin Them Bones: Game Programming for the Web Generation - 1998
Skinned Mesh Export: Optimization - 2007
Tutorial 9: Skeletal Animation