Every key has one or two tangents that control the interpolation of the animation curve. The term interpolation refers to the estimation of values that determine the shape of the animation curve between two keys.
Whether a key has one of two tangents depends on the location of the key on the animation curve. The first key only has a right tangent that controls the interpolation of the animation curve after the key. The last key only has a left tangent that controls the interpolation of the animation curve before the last key.
Dragging a tangent may also change the interpolation mode of the animation curve. For example, most keys are set to the Clamped Auto interpolation mode which automatically smooths animation curve as it passes through the key. If you drag a tangent of a key set to Clamped Auto, the interpolation mode changes to Free Smooth.
The term interpolation mode refers to the interpolation algorithm that determines which shape to use when drawing the animation curve.
To view the interpolation mode for a key, select the key and right-click. The context menu shows the interpolation mode. To change the interpolation mode for a key, select the key, right-click and select another interpolation mode.
Some interpolation modes break the left and right tangents so that you can position them separately. When tangents are broken, you can set a separate interpolation mode for the animation curve before the key and the animation curve after the key. For more details on the different interpolation modes, see Editing Curves. In the Animation window documentation, the interpolation mode is referred to as tangent type.