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When calculating the equilibrium constant, the products are in the numerator and the reactants are in the denominator. Therefore, the greater the concentrations/partial pressures of the products, the larger the equilibrium constant. When the equilibrium constant is greater than 10^3, we say that the products are preferred because there are more of them compared to the reactants.
When analyzing the equilibrium constant equation, we can see that the concentration of products is over the concentration of reactants. Therefore, the bigger the number, the larger the ratio between products to reactants is, or the more product is compared to the reactants. So, when the equilibrium constant, K, is larger than 10^3, that means there is a significant favoring of products since the concentration of products are 1000 times more than the concentration of the reactants.
It can be helpful to visualize the concept of K in terms of the cube diagram Dr. Lavelle showed in class. K is a ratio and for the ratio to show any significant favor there would have to be a majority of the cubes in either color. And thinking of a 10x10x10 cube 10^3 would be the majority of the cubes.
In simple terms, K represents the ratio of concentration of products over concentration of reactants. You have a fraction and if the number on top is larger, your K will be really big, versus if the number on the bottom is really big then your K is going to be really small. So if your K is a really large value (10^3 or larger) then it favors your products and vice versa.
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