The Uncertainty Principle always speaks of two measurements taken as a inseverable whole.  Position and momentum.  Energy and  time.  Angular position and  angular momentum.  The quantum uncertainty of one (the uncertainty of the measurement  when the measuring instrument is perfectly precise) is always tied to the uncertainty of the other.  The product of the two uncertainties--say of position and of momentum--is a fundamental constant of nature.  How accurately we choose to measure one of the two is an arbitrary decision on our part, something like the arbitrary decision of which streets are the zero-streets for house numbers.   It affects the numbers, but it doesn't affect the reality represented by the numbers.

The vertical dimension represents position--in the x-direction.

The horizontal direction represents momentum (velocity X mass)--in the x-direction, P_x.

For a particle, a point in this (blue) space represents: a value of position (x-component only) and a value of  momentum (x-component only). 

X can vary from the value at the bottom edge of the blue to the value at the top edge--It's being held there by impenetrable walls. 

The value of the momentum is limited by the energy the particle has--but it will be constantly  shifting that momentum from direction to direction (x, y, and z): Here we look only at the x-component.

At any instant, the particle has an "uncertainty box" which might be very tall and somewhat narrow, or very wide and not tall at all, or it might be kind of square.  Tall boxes represent relatively uncertain values of position and relatively certain values of momentum.  Wide boxes represent more certainty in position, less in momentum.  Square boxes represent balanced uncertainties.

The uncertainty principle is the observation that all the boxes have the same area no matter what their shape.  That area is 1.0545 X 10^-34 joule-seconds.  The orange-ish boxes scattered on this page all have the same area, but different relative uncertainties of position and momentum.

The total number of those boxes which can fit into this blue box is the number of different ways the particle can be in the state we are examining, the more there are the more probable that state.

The calculation of entropy from the uncertatinty principle works like the calculation of the odds of rolling various values, from 2 to 12, in a single roll of a pair of dice.  We count the different ways things can be that are equivalent: with the dice there is only one way to roll a 2 or a 12, and there are many ways to roll a seven.  (How many ways?) 

Calculating entropy involves counting the many possible states that are equivalent.  Before quantum mechanics we would expect the number to be infinite using such an approach.  But  those "uncertainty boxes" are a limit to the number of states we can distinguish between.

The simplest case for entropy is a particle confined to a box of known dimensions, and having an energy of known value
Just like the number of ways of rolling seven with a pair of dice--or rolling a two-- tells us the relative probabilities of getting the various values on a roll, the number of values of position-momentum--or of time-energy--tells us which condition (state) a system of particles has the highest probability of actually being in.