Complex sentence: Type-II superconductors, besides the Meissner state, possess another state: a sufficiently strong applied magnetic field can produce quantum vortices which can carry magnetic flux through the interior of the superconductor.
Split into simpler sentences: Type-II superconductors, besides the Meissner state, possess another state: a sufficiently strong applied magnetic field can produce currents in the interior of superconductor due to formation of quantum vortices. The vortices also carry magnetic flux through the interior of the superconductor.