B. The sentence is incomplete because it lacks a complete predicate.
A complete predicate basically is what tells you what the subject (pirate) does. When looking at this sentence, a great deal of it is nonessential/parenthetical. Specifically, all that information is serving as an adjective clause describing the pirate. Let’s look at the sentence, now, with the nonessential/parenthetical in bold:
The pirate who sailed his ship in the Atlantic Ocean pilfering from British naval ships and irritating the British navy
Thus, we are still left with the question, “What did the pirate do?”