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 type, 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.
Carbenes can do many reactions. They can be both electrophiles and nucleophiles. They like doing addition reactions on double bonds. They are also found in cheletropic reactions.
Most carbenes are very unstable. However, some can exist for a long time. A famous example is Grubbs' catalyst, which was developed by Robert Grubbs.