The Planck constant led directly to the discovery that nothing
in the physical universe is strictly continuous; instead,
everything is quantized.
The Planck constant reduced by dividing by 2π
(ℏ or h-bar)
is the quantum of angular momentum
(the smallest possible piece of orbital or rotating energy)
and helps determine the sizes of the Bohr magneton
and other neat little units of our universe.
See also in The book of science:
Readings on wikipedia: