A lot of Star Wars fans have been accusing the writers of making Rey a Mary Sue, or a "wish fulfillment" character. I already take issue with this, as the term's primarily used to diminish strong female characters and invalidate the interests of female audiences. While I don't think it's any more fair to call Rey a Mary Sue than it is to call Luke Skywalker one, the main thing adding fuel to the haters' fire is the fact that Rey defeated Kylo Ren in battle at the end of The Force Awakens with no lightsaber or Force training at all. And true, after Rey woke up from her little snow nap, it seemed a bit like she was hitting the "That was easy!" button in whooping that overly-tall angst baby's butt, considering how Kylo Ren is a feared Sith who blows up planets for breakfast. But if you were paying attention, the fight actually makes perfect sense.
The truth is that it was not a fair fight at all. The combatants may be equally powerful in the Force — hell, Rey might even be stronger than Ren — but viewers are right in saying that at this point in the game, she shouldn't be able to take him on when he's in top-notch form and win. But she didn't. There were several factors that helped our heroes out, and which made Rey's victory not only believable, but a little bit inevitable. Consider the following:
Kylo Ren Got Shot By Chewbacca — Hard
Right after homeskillet murders Han Solo, Chewbacca tears him a new one with his bowcaster. Let's consider for a moment exactly what that means. Chewie's bowcaster is notorious for tearing sh*t up. Nobody says it more eloquently than Tumblr user shaochilong-maortuensis, who points out that, in prior films, this weapon has killed people with one shot and shredded an entire vehicle. So Ren got up from a shot that would have murdered any other man, walks it off, and then goes down into the forest to fight Finn and Rey as he is leaking blood all over the place.
Which brings us to another interesting point: Ren beats that wound with his fist mid-battle, seemingly worsening it right at a critical juncture. You'll recall how he still "feels the pull of the Light" (ugh, can the Light just stop calling and leave a voicemail?), and it clearly infuriates him. The Dark Side of the Force draws its power from pain, so in worsening his pain, he was rallying to kick some more of our precious main characters' butts. Unfortunately for Ren, that last-minute hustle didn't end too well for him.
Rey Isn't Exactly An Amateur
It makes sense that Ren pretty much KO'd poor Finn after a minute or so. Not only is Finn not a Force user, but literally everything he knows combat-wise was taught to him by the First Order. Of course Ren is going to anticipate everything he does and, as Liz Lemon would say, Shut It Down.
The showdown was clearly going to happen between Rey and Ren after that — and it's not like Rey beat him very cleanly. There was a huge struggle to overpower each other. And yeah, Rey didn't have any formal lightasber training, but don't forget that she habitually defends herself with a staff. How else would someone of her size and species have survived for all her years alone on Jakku?
So between Rey's experience with the staff giving her an edge, despite her inexperience with using the Force, and Ren's organs basically falling out of him, they were pretty matched, combat-wise. And Rey only defeats him in the moment that she finally manages to harness the Force.
Kylo Ren, For Whatever Reason, Was Clearly Not Fighting To Kill
Let us not forget that, for whatever reason, Kylo Ren doesn't want to kill Rey. In their first encounter, he basically lays out the Kylo Ren Red Carpet of prisoner-taking, carrying her into the ship himself and being significantly less violent with her than he was with Poe (albeit still an ass). Several other lines in the movie cue that he may already know who Rey is, including the lines "What girl?" in reference to her, and the way that he knows that she'll become more dangerous the longer she is set loose in the base after her escape.
But most importantly: He could have killed Rey on the edge of that cliff when they were at a standstill. Instead, he takes a pause to, of all things, offer himself as her teacher. Rey refuses, and takes this crucial moment to harness the Force and deliver the blows that just about finish Ren.
All this seems to indicate that Ren wasn't fighting to his full ability not just because he was weakened, but also because he had other objectives in mind. When you factor in all this, it makes perfect sense that Rey defeated him — the conditions were all on her side, and for whatever reason, so was Ren. I suppose we're just going to have to wait until the next movie to find out exactly why.