The Phoenix Force is ancient cosmic entity that exists as a embodiment of life itself, together with creation and destruction. It is indestructible and exists in all realities of all universes. The Phoenix Force is the core of all psionic energy that has or will ever exist. The force does not have any physical form, so it takes on hosts that are capable of manifesting its powers.
In the story of Jean Grey, the Phoenix Force returned to Earth after it was able to detect a human mind so different, so powerful, that it resonated with the Phoenix's energy. This mind belonged to a young Jean Grey who had no idea of her full potential or how to properly control her powers, and it was when she was trying to telepathically communicate with her dying friend Annie Richardson to keep her soul from going into the afterlife. In her attempt, Jean's mind drifted with Annie's soul into the afterlife, and Phoenix used its energy to break the connection. Ever since that incident, the Phoenix became somewhat fond of Jean and kept a close watch over her.
Many years later, while Jean is on a space mission with her comrades, she gets hurt pretty badly. Dying, she calls out for help with her mind and the Phoenix Force immediately heard the cry. As she was dying on board the space shuttle, Phoenix appears before her and offers to help her. It forms a human shape that resembles Jean herself, and tell Jean to take her hand, and upon doing so, she would get whatever her heart desires. Jean's desire was only to save herself and the X-Men, and she took Phoenix's hand, believing that she will receive what she was promised, and immediately fell unconscious. As a result, Phoenix took the form of Jean Grey with her memories and personality mostly intact. She then saved the X-Men when the ship crash landed and put Jean in a cocoon-like case under the ocean, where she would eventually fully heal but remain unconscious in what is known as a suspended animation. Phoenix then takes her place in the X-Men.