At first, Alonso, King of Naples, represents the false, backstabbing world of court politics that Prospero left behind in Italy. He ascended the throne after Prospero was so unceremoniously deposed. Although Alonso wasn't the major player in this treasonous plot, he still went along with it, and he was the main beneficiary.
Nevertheless, Alonso comes to regret the part he played in the coup of Prospero. His change of heart is indicative of a man who responds to events—both back in Italy and on the island—instead of shaping them. Alonso is so wedded to the temporal world, the world of sight and sense, that he lacks the imagination to comprehend what's going on around him.
It's also notable just how easily mislead he is, and he is a bad judge of character. In political terms, the significance of Alonso is that he represents the dangers—ever-present in Shakespeare's day—of a sudden, unlawful seizure of power. It takes quite some time, but eventually Alonso expresses remorse for what happened to Prospero and the part he played in it. Shakespeare wants his audience to learn from Alonso's mistakes, take their destiny in their own hands as Alonso fails to do, and pledge their never-ending loyalty to the rightful monarch.