Linked from
The 17 pages that link to Fine-structure constant, each with the reason it gives.
Lamb shiftRelated: Its small value organizes the perturbative corrections responsible for the shift.
Physical constantBroader topic: It quantifies electromagnetic coupling without depending on units.
Bohr radiusRelated: Together with the electron Compton wavelength, it fixes the Bohr-radius scale.
Electron massRelated: Precision comparisons involving this constant help determine electron mass.
Heaviside–Lorentz unitsRelated: In these units it is commonly written as e² divided by 4πℏc.