On the trench run, Darth Vader remarked that the Force was "strong with this one", probably not knowing the pilot was Luke. I know Luke is a main character in the movie and couldn't die (so the story could progress) but I assume the Force made it hard for Vader, or anyone else for that matter, be able to hit him.
Why did the Force make it hard for Vader to hit Luke on the trench run?
Using the Force allowed him to maneuver in and out of the TIE fighter's weapons lock, preventing him from being hit. It also helped him to evade the blaster fire coming from the wall positions and tower.
Suddenly, time seemed to slow down. Luke felt not as if he were racing through the Death Star’s trench at full throttle, but rather that the trench was flowing past and around him. He was aware of the pursuing TIE fighters and the weapon-laden trench walls, but he no longer felt threatened by them. He was in control, and he was not afraid.
Darth Vader sensed the change that swept over the pilot in the remaining X-wing. As Vader tried to lock onto the Rebel starfighter with his targeting computer, he said, “The Force is strong in this one!”A New Hope - Junior Novelisation
Obi-Wan: Remember, a Jedi can feel the Force flowing through him.
Luke: You mean it controls your actions?
Obi-Wan: Partially, but it also obeys your commands.
The Force is strong with Luke, even before he becomes a Jedi. It obeys his commands and controls his actions and allows him to fly the X-Wing more skillfully than he could without the connection to the Force. With the Force as his ally, Luke can sense (sub-consciously at this stage in his training) the future and this allows him to avoid the station defences and the TIE fighters.
As Qui-Gon says of Anakin:
He can see things before they happen. That's why he appears to have such quick reflexes. It is a Jedi trait.
Vader is also very sensitive to the Force and knows what a pilot can do when the Force is with him. He can recognise that the pilot of this X-Wing is a Force user, albeit an untrained one.
