The NWID (or Domain ID) was the parameter used in pre-802.11 wireless systems to create logical networks on the shared medium. 802.11 systems use the ESSID (or variations therein) for this purpose.
An interface will usually have a desired logical network associated with it; any packets received that are not associated with this will be dropped, and will increment the 'invalid nwid' counter. The name could now be considered anachronistic.
An increasing 'invalid nwid' counter means that there are other stations transmitting on the channel, or channels that are not completely orthogonal to it. It is an indication of increased use of the channel.