What does it mean to say "Gravity is the weakest of the forces"?

When we ask "how strong is this force?" what we mean in this context is "How much stuff do I need to get a significant amount of force?" Richard Feynman summarized this the best in comparing the strength of gravity - which is generated by the entire mass of the Earth - versus a relatively tiny amount of electric charge:

And all matter is a mixture of positive protons and negative electrons which are attracting and repelling with this great force. So perfect is the balance however, that when you stand near someone else you don't feel any force at all. If there were even a little bit of unbalance you would know it. If you were standing at arm's length from someone and each of you had one percent more electrons than protons, the repelling force would be incredible. How great? Enough to lift the Empire State building? No! To lift Mount Everest? No! The repulsion would be enough to lift a "weight" equal to that of the entire earth!

Another way to think about it is this: a proton has both charge and mass. If I hold another proton a centimeter away, how strong is the gravitational attraction? It's about $10^{-57}$ newtons. How strong is the electric repulsion? It's about $10^{-24}$ newtons. How much stronger is the electric force than the gravitational? We find that it's $10^{33}$ times stronger, as in 1,000,000,000,000,000,000,000,000,000,000,000 times more powerful!

When we say that gravity is much weaker then the other forces we mean that its coupling constant is much smaller than the coupling constants of other forces.

Think about a coupling constant as a parameter that says how much energy there will be in per "unit of interacting stuff". This is a very rough definition but it will serve our purpose.

If you determine the coupling constants of all different forces, you discover that, in decreasing order, strong, eletromagnetic and weak forces are much, much stronger than gravity.

You need around $10^{32}$ (that is 100,000,000,000,000,000,000,000,000,000,000) times more "stuff interacting" to get around the same energy scale with gravity if you compare it with the weak force. Moreover, the difference between strong, weak and electromagnetic forces among themselves isn't nearly as extreme as the difference between gravity and the other forces.

Gravity seems stronger because it's always attractive. Of the other 3 interactions:

• Electromagnetism has positive and negative charges, so it only manifests macroscopically when there is a charge imbalance.
• The weak and strong interactions are intrinsically short-ranged.