Good question! A carbanion is the conjugate base of a carbon acid. In the most simple form, consider a methane molecule (CH4) losing a proton (H+). Whenever you lose a proton in acid/base chemistry, you are losing a hydrogen atom, but the lone pair stays with the conjugate base. So the conjugate base of CH4 would be CH3-, or in other words a carbon atom that is trivalent (connected to three hydrogen atoms via single bonds) with a negative formal charge. In order for the carbon to possess a negative formal charge and have three bonds, it must have a lone pair.
