Melissa was physically exhausted after her fight with Jack and succumbed to her wounds. In her dreams, she met her younger self, the "spirit" of the original character aka Baby Melissa. Baby Melissa is crying and acts like a brat but ultimately confides she wants to be loved by someone. Shes convinced that Prince Ian is that someone, with him being her fiance and the crown prince and all that fairytale jazz.
Without getting too much into details (due to my subpar Korean vocab), this scene highlights the difference between the original Melissa, who chased love and acceptance from those who would never give it, and the reincarnated Melissa, who is beginning to make genuine connections with others (ie Nine, Yona, potentially Yuri from the cover art) and finding her own strengths (sword fighting).
Ian is mentioned only because that's who Baby Melissa focused all her hopes of finding reciprocal love onto, but reincarnated Melissa points out the flaws in that logic pretty quickly.