Think of it as dragon slayer magic being like radiation that changes the body, kinda like with superheroes. Stronger muscles (physical strength, which is why most dragon slayers specialise in martial arts), stronger lungs (magic roars), stronger stomachs (magic absorbtion, they sure as hell need them with their strange diets), stronger skin (magic resistance). And then there is Dragon Force, which just magnifies all these enhanced attributes.
You get it through training with a dragon parent, by implanting a lacrima, or both. Those are first, second and third gen dragon slayers respectively.