The #NO_2# species is a radical species, which displays a lone electron (somewhere!).
The Lewis structure demands charge separation: the nitrogen bears a positive charge, and one of the oxygens bears a negative charge.
#O=N^(+)-O^-# is a neutral species; there is a single lone electron on the nitrogen atom, and, given that there are only 4 valence electrons associated with this centre (6 electrons in total), nitrogen bears a positive charge. On the other hand, the singly bound oxygen owns 9 electrons (rather than the normal 8), and bears a formal negative charge.
#O=N^(+)-O^-# undergoes dimerization, in which the lone electron on each nitrogen couple to form a nitrogen-nitrogen bond:
#2NO_2 rightleftharpoons (""^(-)O)O=N^(+)-^(+)N=O(O^-)#
