Meissner effect: All magnetic fields are reflected back from superconductor (a perfect diamagnet) that holds up magnet that emits the magnetic field in first place (provided the field is not too strong to destroy superconductive state).
Earnshaw's theorem says no STATIC arrangement of electric (or magnetic field) can hold up charges in equilibrium, so the floating doesn't happen for two bar magnets
Meissner effect: you can image: in the superconductor, it has large current loop circuit. The loop circuit can generate a counter force against the outside magnetic field.