The walker sword is a sword. Unfortunately, due to a lack of legs, it is incapable of walking, making its name slightly off-putting.Slightly better than a Diamond sword.
In the latest versions, its abilities are different. If you manage to parry an arrow or bullet or similar projectile, the sword will teleport you instantly to the place it was fired from. Snipers gonna snipe.
In older versions, if you sneak (left shift by default) and right click with the sword you are able to teleport a short distance whereever you happen to be looking at a cost of one durability point of its 2048 durability points.