A carbene is a molecule with a carbon atom that has two bonds and two other electrons that do not make any bonds. Since the carbon has only 6 electrons around it, it is quite reactive. The general formula can be written as R-(C:)-R'.
A carbene can be a singlet or a triplet. In the first case, the two electrons that do not make bonds are like a lone pair. They both stay in the same orbital. In a triplet carbene instead, the two electron stay in different orbitals. Here they both have the same spin.