What is the physical significance of the Planck's constant?
Planck's constant describes the behaviour of particles and waves on the atomic scale. The idea behind its dicovery, that energy can be expressed in discrete units, or quantized, proved fundamental for the development of quantum mechanics.
A glass of water, for example, contains a staggering amount of water molecules; it can be said that the smallest unit of water is a water molecule. Imagine that energy behaves the same way - it comes in "smaller units". Planck's constant links a particle's frequency with its total energy.
Planck introduced the constant in his description of the radiation emitted by a blackbody (a perfect absorber of radiant energy). The constant's significance, in this context, was that radiation (light, for example) is emitted, transmitted, and absorbed in discrete energy packets.
Here's a video on blackbody radiation and Planck's constant: