Great answer, sleeeve!(especially the part about IceCat's hardwork )
Here's a sequence of images to help illustrate your point.
In order to allow movement, the individual elements within the pictures have to be created on separate layers. A number of different software programs will allow you to keep different parts of a bitmap image separate from each other so that their size, placement, and transparency can be adjusted individually.
The four separate elements in the Teddy Bear sequence (listed from bottom layer to top layer) are:
- background bushes
- the bear character
- foreground bushes
- the TeddyBear title
Once all of the images are sequenced you can combine them into a single gif89a file (*.gif). Like sleeeve says a special piece of software is required to combine the images and control the timing/looping. A good piece of software is Gif Construction Set Professional. The learning curve is a little on the steep side and you have to play with it for a while.