I'm a little confused as to how the curve editor is representing the motion of a bone.

if you select one keyframe and start messing with the curve editor window. Is it adjusting the Ease INTO that key? or out of it? or the area between that key and the one before it?

for example. if you have 3 keyframes of a ball bouncing.
1-on the ground
2-top of the arc of the bounce
3-on the ground

To make the top of the arc bounce keyframe transition smoothly, what should the graph curve window look like?

Does the theory of the graph editor change if you select multiple keyframes?

According to this (bottom of page):
http://esotericsoftware.com/spine-documentation/

It controls the ease from that key into the next one.
You seem to also be able to see a curve between that key and the next one on the timeline (I guess just to show it's a belzier curve when you set it).

If you want the ball to slow down as it hits the top of the arc, you want to make the curve steep in the left corner and flat in the right corner.
So.
Key 1. steep in the left corner, flat in the right.
Key 2. flat in the left corner, steep in the right.
Key 3. same as key1
This would be for a bowling ball which is stiff, else the start of the curve would be slightly flat to make it look like it "squishes" a bit before bouncing up.

If you have multiple keys selected it will apply the same graph to all of them if you have "Match" enabled.

In the dopesheet the lines drawn between the keys denote what kind of tweening is done. If there is no line, it means there is no change between keys.

Thx Shui

I'm so used to graph editors in software like maya/3ds max so i was getting a bit confused.

i didn't realize there was curves visible between each keys on the dopesheet. thats cool

I'm a Softimage user myself and have been doing 3D for the last 15 years so I know where you are coming from. We decided to simplify the graph editing a bit for various reasons. Maybe later on it will be improved to actually draw the curves on the entire timeline, but this is a pretty major change.
We do have some improvements coming up to the graph editor though

It'll be a great addition to improve the curve editor. It's a major functionality for animation and actually it's a bit.. difficult to manipulate

If I want to do a simple bouncing ball, how i can have the same In/Out tangent on 1 keyframe? And how I make a tangent perfectly "horizontal"?