Tweening is a special word, it comes from the phrase In Between. It basically works like this, you set two points, for example a start point and an end point for movement. Then you set the time you want your object to move between these points. AppGameKit will then do the calculations of how the object needs to move IN BETWEEN these points for you and move the object.
I am using it in my Sokoban clone. When the character moves I first get the position where he stands and the position where I want him to walk, then set up a TweenSprite for the movement, a duration of 0.3 seconds and AppGameKit will then move the player character for me. It turned out to be very useful.
I've also used tweening for animating text on the title-screen. Once you get your head around it, it's really powerful. You can do a lot more than just move objects, you can scale them, rotate them, change colours and such. I think a tween chain is a way of playing several tweens one after the other.
