Shaders provide us with the ability to leverage the massive parallelism offered by modern graphics processors. Since they have the ability to transform the vertex positions, they can be used to implement animation directly within the shaders themselves. This can provide a bump in efficiency if the animation algorithm can be parallelized appropriately for execution within the shader.
If a shader is to help with animation, it must not only compute the positions, but often we need to write the updated positions for use in the next frame. Shaders were not originally designed to write to arbitrary buffers (except of course the framebuffer). However, with recent versions, OpenGL provides the ability to do so via shader storage buffer objects and image load/store. As of OpenGL 3.0, we can also send the values of the vertex or geometry shader's output variables to an arbitrary buffer (or buffers). This feature is called Transform Feedback, and is particularly useful for particle systems...