What is the significance of the fact that the gravitational constant, G, is a very small number and that Coulomb's constant, k, is a very large number?

Both are constants used in the definition of Forces (gravitational and electric, respectively)

Since those constants are proportional to the magnitude of the forces:

Having a small gravitational constant explains why there is no apparent force of attraction with objects of considerable low mass (they would need to have great value of mass for the equation to give an apreciable force)

Electrical interactions are usually strong, and thus require an appropiate constant to depict the phenomenon. We deal in this case with charges really small, but the forces are in different order of magnitude.

The comparison indicates that the gravitational force is a much weaker force than the electromagnetic force.