The Tangent Actions toolbar provides tools for unifying and breaking animation-key tangents.
By default, when you create an animation key using the Auto-Tangents default, its two key tangents (or handles) are colinear, so that the curve flows smoothly through the key. Using these tools, you can allow the handles to move independently by breaking them, or return broken tangents to unified status. If the handles are not colinear when you unify them, the minimum angle between them is maintained when you manipulate either one (it can be exceeded depending on how you move the handles).
Select the keys you want to adjust before you use these buttons.