Chemical equilibria and changes in concentration
Assuming the following reaction:

$$\ce{A + B &lt;=&gt; C + D}$$

Where:

$$K_\text{c}=1.23\times10^{-2}$$

We say that:

$$K_\text{c}=\frac{\ce{[C]*[D]}}{\ce{[A]*[B]}}=1.23\times10^{-2}$$

And the reaction will be at equilibrium for any concentrations (actually, it should be activities, which are in essence effective concentrations) of A, B, C and D that satisfy the above.

I can understand your confusion. What they mean is... If you have a reaction at equilibrium, and remove half the reactants, then the reaction will proceed towards reactants, until equilibrium is once again reached. 


  Their way of saying it:


You remove reactants, and the position of equilibrium is shifted towards the left, because the reaction will now proceed towards the left hand side to restore equilibrium. 

It's confusing, because equilibrium occurs at the same conditions as before, so you haven't really shifted the equilibrium position in the way it sounds like.