The Broadsword can block by right-clicking. This block works like a normal sword in that it blocks half of all incoming physical damage. It does not block true damage such as being on fire, potions of harming, poison, Rapier attacks, etc.
Broadswords, like other tools in the Tinkers' Construct mod cannot be enchanted, and cannot be repaired at the anvil or Enchanting Table. They can be modified and repaired at the Tool Station, however.
Blocking with the broadsword does not trigger a shield and the broadsword will not show up on your back.