Their eyes need a certain amount of time to fix on an object while they are moving. That bob is the only means they have to get a fix on something for the 20 milliseconds or so it takes since their eyes don't move like ours do. With the visual information they get by doing this over and over, their brain can put together a view of the world on the ground that is steady and makes sense for them.

Brains, be they pigeon or human, form a visual awareness by selectively picking and choosing from all the information that comes from the eyes and even filling in the gaps with "guesses" and reducing visually confusing things like the effects of eye/head motion. It's not like a monitor hooked up to a raw camera feed that shows everything, including the movement involved when the camera moves around. The birds likely don't "notice" the movement visually too much.