A VDZ basis set from the Pople school. Very popular, often used with a set of heavy-atom polarization functions (see 6-31G*). The "6" indicates that each core basis function is built using six primitives. The "3" indicates that the inner valence basis functions are each built using three primitives. The "1" indicates that the outer valence basis functions are each built using a single uncontracted primitive. The "G" stands for "Gaussian", indicating the type of primitive function. (Recently-developed basis sets don't include the "G" or its equivalent since they are essentially all based upon Gaussian functions.)

This definition is in context to Quantum Chemistry. See more contextual defintions for 6-31G.