A dimensionless number, α = e2/4πε0hc = 1/137.03599

This number determines the strength of the electromagnetic force. More accurately, it governs how strongly a charged particle will interact with that force (i.e. absorb or emit photons).

This is one of the primary physical constants that determines the nature of the Universe. If it were a different value, electrons wouldn't orbit atomic nuclei in quite the same way, if at all.

If it were larger, you wouldn't be able to tell the difference between matter and radiation.

If it were smaller, particles might as well ignore the electromagnetic interaction.

Remember, however, that some of the constants in the formula above have dimensions based upon arbitrary human units; the value might not be as serendipitous as it first appears (the anthropic principle).