What does it mean that an orbital is nonbonding? With what do they correspond within Lewis structures?
The orbitals which are currently not participating in bonding are called nonbonding orbitals.
The main role of the nonbonding orbitals is to hold electrons that were not used in bonding. Generally, orbitals which would participate in bonding have a bonding pair of electrons in them, but in the case of non bonding orbitals, they are not using them at the time.
You can simply understand that the lone pair of electrons reside in the non bonding orbitals.