The removal of deadwood is an important task in maintaining the health of a tree and ensuring the safety of people around it, which of course is also a liability issue in urban environments. Deadwood is created as part of a defense mechanism by the tree and naturally it just eventually rots away and falls to the ground.
This is not only extremely dangerous to people underneath but the deadwood itself provides a habitat for insects, borers and parasites that could potentially infect or harm the tree. For both these reasons the deadwood needs to be removed and although it is an extremely time consuming task (i.e. some trees take longer to deadwood than to remove) it is often carried out on a bi-annual basis for many significant trees.