Actually, most people can jump higher, because they don't know how to jump properly. Most people don't know how to stretch properly, or how to engage momentum properly, or how to break past basic mental blocks in movement. Training can teach anyone that. You can go past that and also train precision jumping, or skills that build on jumping like wall-running, or something more simple like jump-rope skills, or something difficult like flips.
In addition to the skill of jumping, jumping with weight will gain muscle and endurance. It also improves the fast neurologic response that is required for the complex series of movements when changing direction. It also trains specific muscle fibers in ways that aren't in strength training.
Much like squatting, all you have to do to start is to jump a lot. Trainers can point out how to optimize your jump. But a lot of the potential to get high air, land on top of something, or reach something high, is mental.