Your title mentions Planck's constant. Planck introduced his constant when he posited that
That is, that energy is proportional to frequency. The constant of proportionality, Planck's constant, is required to convert between our unit for frequency and our unit for energy.
The numerical value reflects our man-made systems of units, and not any fundamental property of nature. In fact, a convenient system of units sets $h=1$, thus using identical units for energy and frequency.
You also ask about the Planck mass and Planck length. They are quantities of unit mass and length constructed from the fundamental constants $h$, $c $ and $G$. Their numerical values reflect man-made systems of units, and in convenient systems, they may be set to one.