He is an antihero in the first film, an antihero turned minor character in the second film and an important character in the third film.
The Curse of the Black Pearl
He is the governor of Port Royal and the father of Elizabeth Swann. In contrast to his strong-willed daughter, he is something of a milquetoast. Both Elizabeth and the Governor sailed from England to the Caribbean eight years prior to the events of Curse of the Black Pearl, along with then Lieutenant James Norrington, presumably when Swann assumed the governor's post. Swann is a doting father, and he wishes for his daughter to accept Commodore Norrington's marriage proposal. However, he eventually comes to accept that she truly loves Will Turner. According to the Pirates of the Caribbean Visual Guide, Elizabeth's mother died when Elizabeth was a young child. It is possible that Governor Swann holds some sort of peerage, as his butler refers to him as M'Lord. Many Colonial Governors held peerages or knighthoods, however, it is not directly stated in the films whether Swann holds one.
Dead Man's Chest
In Dead Man's Chest, he protested a the fact that Will and Elizabeth were arrested by Lord Cutler Beckett for freeing Sparrow and Swann informed Beckett that Former Commodore Norrington had resigned from the Navy, after Beckett freed Will so he could go search for Jack Sparrow, Elizabeth escapes jail with help from her father Weatherby Swann but he is captured by Ian Mercer while Elizabeth is sent off by Beckett to offer Letters of Marque to Jack in return for the compass after threatening Beckett with his life. Later on Port Royal Beckett informs Governor Swann about his Daughter's status and that a EITC ship are in chase of the Black Pearl and that Elizabeth if caught will be saved. Beckett also informs Weatherby that he will be freed as long as he gives good reports to England about Beckett's missions.
At world's End