There’s a German word for it, of course: Sehnsucht, which translates as “addictive yearning.” This is, I think, what these sites evoke: the feeling of being addicted to longing for something; specifically being addicted to the feeling that something is missing or incomplete. The point is not the thing that is being longed for, but the feeling of longing for the thing. And that feeling is necessarily ambivalent, combining both positive and negative emotions.
A paper titled “What Is It We Are Longing For?” published in The Journal of Research in Personality, breaks down these “life longings” into essential characteristics. They target aspects of our lives that “are incomplete or imperfect”; involve “overly positive, idealized, utopian imaginations of these missing aspects”; focus on “incompleteness on the one hand and fantasies about ideal, alternative realities on the other hand”; result in a “temporarily complex experience” combining “memories of the past, reflections on the imperfect present and fantasies about an idealized future” (this is called “tritime focus”); and that “make individuals reflect on and evaluate their life, comparing the status quo with ideals or successful others.”
In other words, your average Pinterest board or inspiration Tumblr basically functions as a longing machine.”