It is the baton of the Constable of France, or rather an imitation of it. The explanation of this particular baton is that William of Orange was originally the disciple and member of the court of Holy Roman Emperor, King Charles V. Charles fought many wars in France and as a sort of propaganda measure Charles let himself out as following in the tradition of the Constables of France, such as Bernard du Guesclin. The emblem of the Constables of France was a plain constable's baton. In the painting below you can see Charles V depicted holding the Constable's baton:
As you can see, it is identical to William's baton. William simply imitated Charles and used the same style of baton, even though he had no intention of claiming to be Constable of France. For William, it was just a plain marshal's baton. Phillip II, Charles' son, and Phillip III, his grandson also used exactly the same style of baton.
In later years, William, who was mentored as a young man by Charles, became his deadly enemy.
To address your question about the symbolism of this baton, you may want to learn more about Betrand du Guesclin and the Constables of France. The Constable was supposed to be the chief of the army under the king, but some of the Constables, such as du Guesclin, were quasi-independent military dictators. These men were sort of like Oliver Cromwell, styled "protectors" of the people. Their sceptre was a plain wooden rod, a watchman's club, because it symbolized their role as being sort of a chief policeman of the country.