A carbene is a species that has a formally neutral carbon atom bearing two nonbonded valence electrons.  A carbene has the following general structural formula.

R¹ and R² could be any ligand

eg:

A carbene could exist in two spin states: singlet carbene and triplet carbene.  In a singlet carbene, the two nonbonded valence electrons in the electron-deficient carbon are in the same orbital, i.e., they are a lone pair.

In a triplet carbene, the two nonbonded valence electrons in the electron-deficient carbon are in different orbitals.  Since a triplet carbene has unpaired electrons, it is, by definition, a radical.

see also carbene equivalent, nitrene