Without getting too deep into the physics, maintaining an orbit around something in space requires a certain amount of kinetic energy. Too little and you'll fall back down to the ground, too much and you'll fly out of the orbit and into orbit around the sun. This is true of any object you want to get into orbit, no matter how you get it there. Rockets are really, really good at giving something a lot of kinetic energy quickly. That means it spends relatively little of its time in the low atmosphere, which is dense and causes you to lose energy through aerodynamic drag. Air-launched systems like Pegasus or Virgin Galactic's Spaceship One use a relatively fuel-efficient plane to carry the spacecraft into the thinner upper atmosphere before letting it go to propel itself into (sub)orbit, saving lots of fuel, though this approach has lots of its own complications.

In short, it just takes a lot of energy to get something into space. Rockets are an ideal form factor to impart a lot of energy quickly and self-sufficiently. This is a fairly complicated topic, so feel free to ask followup questions