This question already has an answer here:
Since $h$ seems to relate to a fundamental unit of quantization, it only seems right that we should have an idea of why it has the value it has. What do we know?
I understand that to some extent the precise values of universal constants are arbitrary, but when I look at the Bohr model, I see that the angular momentum of electrons comes in discrete levels that appear to be directly proportional to Planck's constant. Which suggests to me that there is something special about this number.