We all have seen the first Harry Potter film where Professor Flitwick charms the class by introducing them to the spell of Wingardium Leviosa. This might seem like pure magic but at an atomic level, this is actually possible. Everything in the world around us is never in contact with any object, meaning everything is rudimentarily levitating. As we know, the matter around us is made up of atoms that contain nuclei made up of protons and neutrons with electrons whipping around them. When two atoms come close to each other, the electrons of each atom start to repel each other, as like-charged particles repel, and Coulomb's electrostatic forces take into action. Even though this is a very minor effect in real life, it is a true phenomenon in theory.
This is an atomic approach, but this phenomenon can be better explained through the world of magnets. This is similar to electric charges, but the like-charges can be replaced for a system of two magnets with the like-poles opposite to each other. The magnetic approach to levitation is applicable in the real world where we most popularly see it in use with Maglev, or magnetic levitating trains.