Changes that you have made to a parent object can be added to the children by clicking this toolbar button. Similarly, if you have made changes with Modify Subtree on, and you want to remove the changes from the children, clicking Modify Child Keys will remove those changes from the children that you previously made to the parent.
This tool is primarily designed for use in Dope Sheet Edit Ranges mode.
Modify Subtree allows you to move, scale, edit time, and so on, on all sub-tracks for any or all tracks on a node. Modify Child Keys does the same thing, but also extends to child nodes as well. Modify Subtree lets you edit timing for an object of subset of tracks on an object, while Modify Child Keys lets you edit the timing of an entire linked structure, group, or character.