I see Eowyn in The Lord of the Rings as a type for the Church. She is a warrior, but only fulfilled when she comes to love a gentle warrior, Faramir, thus finding healing in love. That she is attractive as the "shield maiden" and an accomplished warrior herself, and as she fulfils a prophecy by killing the Witch-King of Angmar, her part in the story is not small. Eowyn beings about healing for her uncle as well.
In the movie, Faramir is not shown as Tolkien intended, although the actor is superb. Faramir is a philosopher, a gentle and wise man, the foil for his brother, the total man of action. That Eowyn weds Faramir is a sign of harmony and completion, as she too, is a woman of action, but must become one of meditation and contemplation, which only happens after her brush with death.