stay, many hosts would be only to glad to say goodbye to their guest, however close their friendship. Most kings would also understand that a fellow monarch has matters in his own kingdom to which he must attend. Leontes, however, desperately begs Polixenes to extend his stay and, when he refuses, asks his (Leontes's) wife, Queen Hermione, to persuade him.

Hermione manages to convince Polixenes to stay, but, instead of being pleased at having achieved his aim, Leontes suddenly decides this success must mean that Polixenes and Hermione are having an affair. He even thinks that the child she is carrying really belongs to Polixenes. He tries to have his former friend poisoned, but Polixenes, forewarned, hurries home to Bohemia.

Throughout most of the play, therefore, Leontes and Polixenes are bitter enemies, because of the irrational fears of the former. They are reconciled at the end of the play, when Leontes apologizes for his groundless suspicions.

This play begins with Polixenes' visit to Leontes and Hermione, to demonstrate the history that these two men share.  As the Enotes character analysis of Polixenes says so well:

The two kings have been friends since childhood, Polixenes fondly remembering that childhood as one of carefree innocence as yet untempered by the realities of the world. The two were then indistinguishable in their innocence and energy. Polixenes reminds Leontes, "We were as twinn'd lambs that did frisk i' the sun / And bleat the one at th' other" (I.ii.66-67).

This sameness that they share is important in the play, because it sets up, from the beginning, the notion that every man is fallible and susceptible to acting in regrettable ways.  For Leontes, this irrationally reprehensible behavior consumes the first part of the play through his accusations that his wife and best friend have been having an affair, an accusation that drives Polixenes to flee for home and leads to Leontes killing his son, banishing his baby daughter to be abandoned for dead, and, he believes, killing his wife.

For Polixenes, the irrational and reprehensible behavior comes when the play moves to Bohemia.  He goes ballistic when he believes that his son has chosen a poor, shepherd's daughter for his wife. Unbeknownst to Polixenes, this shepherdess, Perdita, is the right daughter of Hermione and Leontes.

It takes the magic and grace of the final moments of the play, which includes the reconciling engagement of Florizel and Perdita, to bring healing and forgiveness to Leontes and his friend, the man who has also acted reprehensibly, Polixenes.

Both men share a similar journey of self-awareness and the two journeys reflect upon each other to strengthen the overall message of the play.  It is this connection as a sort of "mirror image" to Leontes that gives Polixenes his importance as a character and also gives meaning to his journey as a reflection of that of Leontes.