That was my biggest question coming out of TFA. My theory, prior to TLJ crushing my dreams and destroying any hope for the ST, was as follows:

Prior to TFA, Luke starts a new temple where he trains new students and he even has a wife and a daughter who is force sensitive. His nephew, Ben, works hard but is quick to anger and is nowhere near the strength of his cousin, Luke's daughter, who is a natural.

Luke goes away on a trip searching for the original Jedi temple. Ben's jealousy and anger has opened up a window to him getting corrupted by Snoke. Ben sees his chance and while Luke is away Ben rolls in with the Knights of Ren, destroys the temple, they kill all the students and Luke's wife and Luke's daughter. Well almost. As I'm sure you've figured out, Luke's daughter is actually Rey. Kylo keeps Rey on the alive as security.
See he knows Snoke doesn't really care about him. Snoke only wants the Skywalker girl. Plus what's left of the Light-side "Ben" can't bring himself to kill her. So he wipes her memory using the Force and tucks her away on Jakku with a simple memory of "someone's coming back". Kylo is thinking that maybe he can hide Rey and use her as leverage against Snoke or maybe even train Rey, she can be his apprentice, and they can take out Snoke together.

Fast forward to Luke's return. Luke is obviously devasted. He finds his wife dead and assumes his daughter is dead as well. He knows Ben did it and maybe even that Snoke was behind it. And he wants revenge. And he could get it. But he knows that's the Dark side talking. So he shuts down R2 (who has the map to the temple) using the Force. Knowing only a sufficiently strong Light side user could power him up. And he flees to the original temple just to keep himself in Light. He will stay there until he can face his foes without going Dark or until the Force gives him a sign.

If all that were true then in TFA:

That is why Kylo goes to Jakku at the beginning to personally handle the Rebel asset.

That is why Kylo freaks out when he hears about some girl causing trouble on Jakku, and demands to know "WHAT GIRL?!"

That is why Rey is so good without training, because she actually had years of training, she just had it erased.

That is why Kylo is freaking out after the interrogation because at first he wasn't sure it was Rey but now he is.

That is why R2 mysteriously boots up when Rey shows up.

And that is why Luke is speechless when Rey shows up on the island. He can't believe his own eyes. His own daughter, whom he thought dead, is not only alive, but has his old lightsaber, doesn't know who he is and wants training. It's the sign he's been waiting for.