Junction Machine Ellone is a device that exists in the distant future era in Final Fantasy VIII, though it never made an actual appearance. It was created by Dr. Odine after intense study of a kidnapped Ellone, who possesses the unique ability to send a person's conscience back in time into the mind of another. Dr. Odine created the "Junction Machine Ellone" to replicate Ellone's power, and the device proved successful in doing so, though not to the power and extent of Ellone's own true ability.
The Final Fantasy VIII Ultimania explains that Ellone's ability to connect to the mind of another, is a same kind of process as when a person junctions a Guardian Force; one's consciousness can’t be connected to another without an intermediary with a special ability - a Guardian Force, Ellone herself, or the Junction Machine Ellone.
The machine was used by the main antagonist of Final Fantasy VIII, Ultimecia, in order to send her mind back in time from the future and into the distant past where she was able to take possession of the bodies and minds of Sorceresses Edea, Rinoa, and Adel in order to further her own desires to initiate Time Compression. The structure and appearance of the "Junction Machine Ellone" remain completely unknown, as does the fact of why Ultimecia is capable of possessing only sorceresses.