Actually -- it does mix -- but as you have observed, not easily.

Salt water with a substantial amount of salt dissolved in it is chemically and physically quite distinct from fresh water. First, salt water has substantially higher density (enough that in very salty water like the Dead Sea or The Great Salt Lake, it is very difficult to dive -- human bodies float substantially higher in the water). Secondly, salts like Sodium Chloride dissociate when dissolved in water into Sodium and chlorine ions surrounded by water molecules called ion complexes, which share the heavy ionic potential of the ions. So when you mix the two, (this is easy to see if you dissolve some food coloring into one of them), the salt water immediately sinks to the bottom (so it only contacts freshwater on a small surface) and at this boundary, there is a requirement for thermal energy if the salt water is fairly concentrated, slowing the diffusion of the two. However, if you wait a long while, you will see that they do mix-- this can be hastened by heating or by vigorous stirring... Such mixing will not occur if two liquids are immiscible -- like oil and water.

The reason salt water and fresh water tend to separate is because their densities are different. Density is a useful idea in science. It means how much "stuff" is in a certain amount of space. A can of air has less mass than a can of water that's the same size. So the can of water has a higher density. Salt water weighs more than the same amount of fresh water. This means that fresh water will "float" on top of salt water. This happens when water from rivers flow into the sea.

There are some interesting experiments you can do with salt water. Ask your teacher or parents to help you try this: Take a grape and put it in a cup of water. Usually it will sink. Now try adding salt (or sugar) to the water. How much do you have to add before the grape floats? You haven't changed the density of the grape (you can weigh and measure it to make sure), so why does it float when you add salt or sugar to the water?

In fact, if you pour salt water into fresh water, it does not separate ! It mixes. This is what happens when a river (fresh water) meets the sea (salt water).

Take two glasses, each half full of water. Put in a teaspoon of salt into one of the glasses and stir. Then take a small sip. It will be salty ! Now pour the liquid in this glass into the glass with fresh water, and take a small sip. It will be less salty. You will find that the teaspoon of salt is now perfectly distributed (dissolved) through the entire amount of water.