Superconduction was discovered in 1911 but it was not understood for years do to the lack of a theory to understand it was not yet in place. It turns out that at the critical temperature the electrical resistance suddenly drops to zero. This basic theory is that at the critical temperature electrons become coupled over a ranger of about 1,000 X the spacing of the conductor’s lattice with a binding energy that is the result of vibration that the electrons cause in the lattice. Called cooper pairs, the coupled electrons effectively becomes a boson and condense into the ground state. The result is that each coupled electron helps the other over come any resistance encountered from the lattice.
The Meissner Effect is where a magnetic field is expelled from a superconductor during the transition to the superconducting state that is caused by electric currents generated near its surface by the applied field. The magnetic field of these currents cancels out the applied magnetic field within the superconductor. This causes the magnetic levitation associated with superconductors.
Superconductivity is a purely quantum effect that has no counter part in classical physics. It’s most commonly known effect is magnetic levitation. It is one of two purely quantum effects that are seen on a macroscopic scale.