The X-Men's Jean Grey first encountered the Phoenix Force when she was a teenager, just beginning to experiment with her telepathic and telekinetic powers. Jean Grey is an Omega Level mutant, one of the most powerful telepaths on the planet. She's long been bound to the Phoenix Force, a cosmic power of death and rebirth.
The relationship between Jean Grey and the Phoenix Force was finally explained during the Grant Morrison era. He adapted the theological idea of "apotheosis," of a human transcending their humanity and uniting with a pre-existent Divine being. The teaching was incorporated into the so-called "New Age" movement in the 1960s, the kind of mysticism Grant Morrison has always been fascinated by. He allowed it to inform his New X-Men run, and it was a perfect thematic fit for Jean's arc.
Jean's first brush was the Phoenix Force was revealed in Classic X-Men #42, which featured a flashback story set a few years before the founding of the X-Men. Jean's powers had first triggered under tragic circumstances, when her friend was injured in a car crash and she unwittingly entered her dying mind. The experience had left her in a coma, and she was only brought out of it by Charles Xavier. He spent the next few years quietly training Jean, but began to realize her power was far greater than he had realized. On one occasion during this training, she sensed another mind calling out to her, the mind of a young mutant in pain. On the Astral plane, Jean manifested a Phoenix raptor as a part of her psyche reached out to the boy. It wouldn't be long before she met the teenager in the flesh - Scott Summers, aka Cyclops.
Classic X-Men #42 revealed the secret first encounter between Jean Grey and Scott Summers, and it laid the foundation of a psychic rapport that would only become stronger as the years passed. Both were too young to even begin to understand what had just happened, and they forgot all about this. Cyclops had no idea what had happened, and Jean's memory of all this was erased, because Xavier began to fear her powers. He suppressed her telepathy for years, fearing what it would become, never suspecting Jean was tied to a cosmic force.
The Phoenix Force transcends the normal rules of time and space. It had clearly recognized the future relationship between Cyclops and Jean Grey, and it took compassion upon the future X-Men and brought them comfort at a moment of pain and loneliness.