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The child of constraint is used for creating parent-child type behaviour without requiring an actual parenting (which would change the hierarchy of the bones in an armature).
Some common uses of the constraint are to transfer parent ownership of an object or bone (example), or constrain the orientations of a 'hinge' enabled joint to a root control. For example if the head of your character is set to 'hinge' so it does not inherit orientations from it's parent, you may still want it to follow along when the root bone (the controller for all bones in a character) is rotated. This constraint allows the head to follow the orientations of the root, but still remain a child of the neck (Blend File).
Options and Settings
OB: The Object to serve as the controller (when rigging, it is the name of the Armature Object which contains the controller bone).BO: The Bone to serve as the controller.
Use Channel(s) Loc/Rot/Scale X/Y/Z Buttons These determine which transform channels the constrained bone will use.
Set Offset Performs some fancy matrice math to move the constrained bone to its original position relative to the parent bone.
Clear Offset Removes the offset, moving the bone back to the transformations of the constraint parent. If 'set offset' has already been enabled, it is usually necessary to use 'clear offset' before pressing 'set offset' again if a change is made to the constraint options.
Influence Determines the influence of the constraint as a percentage from 0-100%. This value can be animated manually, or driven by another object or bone in the IPO.
Show Shows the constraint in the IPO window.
Key Sets a keyframe on the current Influence of the constraint at the current frame.
More Resources:
Blender Wiki Page - Child Of
