I think the song is about a failed relationship with someone who once loved you deeply but you didn't love him back as much as he does love you. During the coarse of the relationship, the other showed a greater love for one person while that person didn't compensated the affection and even ended the relationship. In the end, the one who ended the relationship realized that all the while she actually had loved the other person and asked for forgiveness or a reconciliation. The reason why she goes back to December (probably their love relationship started in that month or they had many fond-lover memories during those days) is to keep her from feeling lonely. Reminiscing the past comforted her.