Forces are carried by particles, and as a first approximation, the potential experienced by two objects charged under said interaction is given by the Fourier transform of something like [itex]\frac{1}{k^2 - m^2}[/itex], where m is the mass of the force carrier. For the electromagnetic and gravitational forces, the particles in question, the photon and the graviton, are massless, and the Fourier transform of [tex]\frac{1}{k^2}[/tex] is roughly [tex]\frac{1}{r}[/tex]. On the other hand, the weak and strong forces are mediated by massive particles, and so [tex]m^2 \neq 0[/tex]. The Fourier transform is now roughly [itex]\frac{e^{-m r}}{r}\,[/itex], in other words it is a short range force. This is the correct meaning of short versus long range.
Now there is an additional effect, which has to do with the spin of the force carrier. In the case of the spin 1 force carriers, the photon and W bosons, the potential depends on the sign of the objects in question. Thus positive and negative particles attract, positive and positive particles repel, etc. As nature would have it, matter in the universe is largely neutral, with equal number of positive and negative charges spread out. Thus, over long distances, the electric force is very feeble, because objects are approximately neutral. This is known as screening. On short distances, however, minor irregularities (rubbing amber rods against cats, e.g.) give rise to powerful forces.
This is contrasted to the graviton, which is spin 2, and couples to mass. Barring things with negative mass, the gravitational force is always attractive, and so there is no way for forces to cancel each other out. You can have electrically neutral galaxies but not gravitationally neutral ones. This is fortunate otherwise the electric force would surely dominate.