A polar liquid is miscible with a polar liquid whereas a non polar liquid is miscible with a non polar liquid as like dissolves like. Why is a polar liquid not miscible with a non polar liquid?
Remember the chemistry saying "Likw dissolves like." This is what makes a liquid. There is always some attractive force between like particles. This explains why a non-polar molecule can mix in a non-polar liquid. Polar molecules can polarize and rearrange their orientation to bind and mix.
Let me first clarify two points. The first relates to the usage of terms like miscible: it is not so that apolar stuff is completely immiscible with polar stuff, it is only that there is a very small amount that gets mixed. The second is perhaps more important: what you describe are experimental facts. The only thing we can do is try to find a (minimal set of) rules that aids us in describing what is observed and possibly use to predict the situation for what we have not as yet experimented. There is one set of such rules that originate from molecular thermodynamics that brings back the observed behavior to molecular interactions described in terms of potentials and the like. Then there is the more chemical approach that identifies the behavior of (groups of) atoms in a molecule as being responsible for, in this case, dissolution behavior. For instance, whether a group can dissociate or not.
Therefore, a simple answer to your question cannot be given unless you formulate it more specifically: what kind of molecules are you interested in and which is your favorite point of view?
I should like to Ger Koper's answer that it also depends on temperature and pressure whether substances are miscible or exhibit limited miscibility. Supercritical water can dissolve many hydrocarbons very well. On the other hand, the mixture (nitrogen + ethane) – both nonpolar –exhibits a liquid–liquid phase split at low temperatures.
Mixing two substances, A and B, involves splitting A–A and B–B interactions (which usually requires energy) and forming new A–B interactions (which releases energy). The energy balance of this process is one of the factors that controls miscibility.
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