When the Empire emerged from the ashes of the Clone Wars, Emperor Palpatine ensured they rewrote history in their favor. According to him, the Jedi were the reason the galaxy fell into disarray. Instead of peacekeepers, they were painted as instigators and worse. Besides killing the remaining Jedi in a bloody purge, the Empire also erased traces of the order wherever they could by destroying Jedi Temples. It meant lost history, records, and important perspective. The Empire didn't wreck everything, though. At least one temple is still around in the decades after Return of the Jedi, and it's there that we encountered Luke Skywalker at the end of The Force Awakens.
We'll return to Ahch-To in The Last Jedi, presumably to watch Luke and Rey train and have important discussions about the future of the Jedi Order. Han told Rey and Finn that people thought Luke went searching for the first Jedi temple, and Episode VIII writer and director Rian Johnson confirmed to Vanity Fair that was true. According to Vanity Fair, he "has been living in this village among an indigenous race of caretaker creatures." Johnson specifically called it a little Jedi village. The notion of a temple with caretakers is something we've seen before to a degree on Jedha in Rogue One. The Temple of the Whills on the planet wasn't specific to Jedi, but guardians like Baze and Chirrut watched over the disciples.
Johnson's statements confirm Luke was looking for the first temple, but not whether Ahch-To is that place. The book Star Wars: Complete Locations tells us Jedi scholars disagree about the location of the first Jedi Order temple. They made cases for the temples on Coruscant, Jedha, Ossus, Tython, and Ahch-To. If you're Luke and searching for guidance about what to do after your best efforts have resulted in sadness and destruction, it makes sense you'd want to try to locate the place it all began.
The first ever Jedi temple could offer some insight into important whys and hows, or maybe Luke is hoping to find the answers to questions about the history and intent of the Jedi Order founders. I think he's a man searching for answers, meaning, and a guiding light. It's easy to understand why he thinks going back to the starting point might hold the truths he's after.
Coruscant Jedi Temple
Our experiences with Jedi temples in the movies, television series, and beyond have certainly been enlightening. There's the obvious location on Coruscant, which we saw repeatedly in the prequel trilogy and in Star Wars: The Clone Wars. The temple was constructed over a Sith shrine and a natural spire that attracted Force-wielders--not only Jedi--back in the day. This temple was sprawling and a place of spiritual growth and study, a place to learn and perfect physical skills, and a place of knowledge. Think of it as the Jedi HQ.
Another temple was located on Ilum. That location, home to kyber crystals, was eventually mined and destroyed by the Empire. We saw Ahsoka take a group of Padawans there to find the crystal for their lightsabers. If you fast forward to Star Wars Rebels, we watched Kanan and Ezra visit Lothal's Jedi Temple because they needed help finding their way. The temples dotted around the galaxy were outposts and/or academies, places for Jedi to reach when they were on missions or before they were more centralized on Coruscant.
Lothal Jedi Temple
Jump into the days after A New Hope, and we followed Luke as he was pulled to Devaron's Temple of Eedit; he used the natural vergence in the Force there to level up his training. After that encounter, we saw Luke searching for other Jedi Temples in the Star Wars comic for the purpose of gaining knowledge. He knows and has experienced what the temples have to offer, which is probably one of the reasons he searches for the first temple years later when he's feeling lost.
In The Last Jedi trailer, Luke said, "I only know one truth. It's time for the Jedi to end." Maybe what he's studied at the first temple and learned from the caretakers led to that statement. He went there to perhaps connect with the past of the Jedi Order. He's turned to the temples in his past for a boost and to gain greater understanding, so why not now?
Has The Last Jedi's mystery man been revealed?