I guess that you're asking about how the heads of pigeons, chickens etc move backward and forwards as they walk...?
In fact, if you watch carefully they don't move backward at all -- it's jerk forward, stop, jerk forward, stop.
Most birds see movement much more clearly than stationary objects. They are able to "lock" their heads stationary with an amazing reflex in their necks (a few mammals can do this too, such as squirrels). Then movements show up more clearly.
If you hold a live chicken under your arm, you can wave it about slowly and its head stays exactly stationary as if it's on the top of a pole. If you push the chicken's head gently with your finger, it feels oddly as if it's bolted down -- it pushes back so quickly and smoothly.
You can see a robin do it too, when sitting on a waving twig. If you watch the head of a hovering kestrel or buzzard, it too remains stationary, with the rest of the bird flapping and dodging about in the wind.
When they are walking, all that is happening is that they are walking along under their stationary head, then as it gets left behind they have to "tick" it forward to catch up quick. As they speed up they stop bothering and hold their heads still relative to their bodies. You notice it more in birds which walk steadily, rather than those that hop like a thrush.