Lyric discussion by Chelle812 

Cover art for Jessica lyrics by Regina Spektor

Regina's birthday is in Feb so perhaps this is her way of serenading a friend that she shares a birthday with.
I love the song and it certainly does have a bittersweet quality to it that gives the song more depth. Jessica's possible depression does sound plausible.

My Interpretation

It actually is about a friend who has a birthday in February who died of cancer.