The tweak node is created for an object as soon as you create a deformer for it. It keeps track of the transformation of the vertices (the deformation) on the object by storing its vertex position information. This ensures the proper transformation of vertices when you deform the object.
When you delete the tweak node, all the transformation information for the vertices that are affected by the deformation is erased, which is an easy way of removing deformations from an object.
See Point tweaking on objects for more information.