This is an opinion article based on Star Wars 7: The Force Awakens, it is simply just my personal speculation on who I think Rey is. This article will contain spoilers from the film as well.
Now that's out of the way, from other theories online about who Rey is it seems that no one has come up with the possibility that Luke Jedi mind tricked or Jedi mind wiped Rey when he was training new Jedi. From this it explains why she is able to access Force abilities. While training his new Jedi it is possible that Luke feels a disturbance within Ben (Kylo) Solo and discovers that he will be betrayed. Luke then takes his daughter Rey on a cruiser to Jakku where when he drops her off, he wipes her memory and tells her that Luke Skywalker is a myth and that the force does not exist. He then tells her that her family will return to get her.
Luke didn't specifically tell her that her mother and father will get her, he just told her that her family will get her. Han and Leia are family. After the whole Ben is now Kylo ordeal, Han eventually loses the Falcon and travels across the galaxy searching for the Falcon in order to keep his promise to get Rey when the time is right. Flash forward to when Finn and Rey escape Jakku on the Falcon, a homing beacon is turned on allowing Han to find the Falcon. Low and behold the Falcon was in Rey's hands making Han's job easier in finding both her and the Falcon.
Jumping to when Rey, Finn, Chewy and Han were at Maz's palace, it's made clear that Rey is a Skywalker when the Skywalker lightsaber calls to her through the cries of the youngling's from 'Revenge of the Sith'. As Rey finds the lightsaber her force abilities are awakened it is unclear to her why or how it is possible and almost denies it, however Luke's mind wipe is then lifted and Rey remembers that Luke is her father all through her visions.
While she is captured and interrogated by Kylo she then remembers how to use the force to prevent Kylo from learning that she is a Skywalker. After realizing but not mentioning that Han and Leia are her uncle and aunt, she is reminded that Kylo is Ben her cousin. This leads to her being so distraught when she see's Kylo kill Han. For those who are thinking, 'Well yeah wouldn't anyone?' and I say yes, but after knowing someone who had such potential and good inside them it leads to a more plunging pain inside, similar to that of Chewy. Assuming Chewy was around while Han and Leia were raising Ben. Chewy probably felt the same as Rey and in even more pain for losing his best friend.
When Han died it's shown that Leia sense's this in the force, there is no doubt that Luke felt this as well. This potentially clouds Luke's mind where he then goes to meditate. When Finn and Kylo are fighting, Luke's meditation is broken by this fight and contacts Rey through the force to tell her that she must face Kylo but not kill him, just show him that she is the rightful owner the lightsaber. This then leads into Kylo and Rey's fight.
Towards the end of TFA we see Rey and Leia comfort each other as Rey now knows the truth about who she is. This is why the Resistance sends Rey to find Luke. Leia probably believes that Rey is the Resistance's best chance to get Luke to come out of hiding. While entering the system Luke feels a strong force presence. When he sees that it is his daughter, he gives her a look as if he's seen a ghost he is simply in disbelief that she found him.