Luke Skywalker's Jedi Temple is an unnamed Jedi Temple located on an unknown planet, sometime after the end of the Galactic Civil War. Luke used this Jedi Temple to train a new generation of Jedi Knights, in order to restore the Jedi Order to its former glory. Unfortunately the Jedi Temple was destroyed by a lightning storm in the night Ben Solo fell to the dark side, and most of Luke's students were killed during this event.
Sometime after the Battle of Jakku, Jedi Master Luke Skywalker discovered or built this Jedi Temple on an unknown planet to serve as a Jedi academy and train a new generation of Jedi Knights, establishing a New Jedi Order. Realizing that the old Jedi teachings as well as the old code were flawed and to avoid the New Jedi Order from making the same mistakes as the Old Jedi Order, Luke altered some of the Jedi teachings and code.
The first of Luke's students was his nephew, Ben Solo, and several other Force-users. Unfortunately, Ben fell to the dark side when he discovered that his uncle wanted to kill him, because Luke was afraid of how strong his nephew's connection to the dark side of the Force was. Ben attacks Luke in self-defense, and collapses the hut they were in. Ben then (apparently) killed most of Luke's apprentices. Unbeknownst to everyone, Ben did not actually massacre all his fellow apprentices, as they were killed by a lightning storm (possibly made by Sheev Palpatine).
The three survivors that were not in the Temple when the storm happened pursued Ben Solo for attacking their master Luke. Two are later killed confronting him and one is murdered by Ren, the former leader of the Knights of Ren.
Luke was in horror for being unable to stop the death of his apprentices, as he and his astromech droid R2-D2 watched the Jedi Temple burning. Luke went in search of the Ahch-To Jedi Temple, as he was guilt ridden over his students' deaths and Ben's fall to the dark side. Luke decided that he would remain in hiding on Ahch-To until the time of his death, so that the Jedi Order would end with him.