Advice from the old lady:
It's about being unique and desirable but yet elusive. That is the nature of a great seducer and let's be real, great seducers are RARE but consistently desirable and consistently elusive.
If you want a full dissertation and well researched tome on the subject read Art of Seduction by Robert Greene. It goes deeply into detail about the psychology of seduction, which of course is the psychology of obsession.
Bear in mind that desirable yet elusive go hand in hand. This reflects emotional unavailability, wanting what one cannot have, etc as noted by other posters in this thread. There is an aloofness about such a person. But there is also that ability to back it up.
Examples:
My husband was obsessed years ago over a girl he met in an internet chat room. She tantalized him over the messages in the chat one night & when he called her out on it she drove 3 hours in the middle of the night to meet him, banged his brains out like a freak all night and then she vanished out of his life never to be heard from again. He never knew her name but he was "messed up" over that girl for months back then and still recalls that whole experience with clarity and awe. But she was an elusive fantasy and based on her behavior she knew that and knew exactly what she was doing. He was merely a conquest, notch & good story to her.
My ex BF of 3 years will never get over me. I was exactly what he wanted but he set the rules and would not be fully committed. Fine. I played by his rules so he was never able to fully possess me and I never ever chased him like other women. He fell deeply in love with me but got physical one night so things ended abruptly.
4 years later I am out with my husband & run into ex BF. He is cordial, wants to be best mates with my husband, trying to catch up with me, his best friend tells me they have talked countless hours about me over the years, I'm the one who got away etc. For 6 weeks after running into him randomly he tries to re-establish contact. He's been blocked for years on everything but he got creative, established new social media accounts and proceeded to full court press me any way he could think of. I never responded to anything. Thankfully he has stopped (I showed my husband everything, total transparency). And I asked my husband to please listen next time when I say it's best not to show up somewhere he goes....
It is a combination of being desirable & yet elusive. Read Art of Seduction.