Jūshin (獣芯?) in the world of Final Fantasy X, is a type of summon apparently akin to an aeon. Unlike the aeons, their appearances resemble humans. It likely is linked to beckonings. In Final Fantasy X-2.5 ~Eien no Daishō~, a companion novel and sequel to Final Fantasy X-2, Yuna and Tidus travel 1000 years back in time to an ancient Besaid where they meet various spirits of ancient summoners from before Yevon adopted the summoning practices as part of its dogma. These ancient summoners worship a different set of deities and created their own fayth via the help of a person they shared deep feelings with. This bond with their personal fayth would allow them to perform summonings, and summon the likeness of the person who was made into a fayth, "Jūshin", who can possess supernatural abilities.
In the novel summoner Kush's guardian, Velm, is in love with her, and wants to be made into her "Jūshin" by dying for her sake. He fails at this goal as he is killed before his time. Kush, who had also loved Velm, never wanted him to become her "Jūshin", and instead wanted to become the "Jūshin" to another summoner, Ifarnal, to free Velm from his duty as her guardian.
It is implied there are various ways in which one can be made a fayth for a "Jūshin". Velm wanted to die for Kush to become one, and in another scene it is implied a sexual act can also create a fayth. The bond the summoner shares with their fayth determines the strength of their summonings, and it is implied Ifarnal didn't have such a deep bond with Kush, as although she became his "Jūshin" he later says the bond is inadequate and he was unable to sustain a prolonged summoning because of that.
During the novel Tidus is killed in a freak accident and Yuna faints from the shock, but when she comes to she finds Tidus by her side. She believes to have beckoned him and that as he is essentially little more than an unsent he is bound to disappear. It is unclear whether this is indeed the case, or if Tidus had, in fact, become Yuna's "Jūshin" and she would thus be able to "summon" him back into the world via the bond they shared.