Question: Why does the addition of a solute decrease the melting point of a compound?
In a word, entropy.
Entropy is a measure of the randomness of a substance. Things that are disordered have high entropies, while things that are less ordered have lower entropy. Generally speaking, the universe tends toward disorder, so things with high entropy are preferred over things with low entropy.
Let's imagine what happens when we dissolve salt in water. What we've got is a more random solution than we started with. Instead of just having pure water, now we've got water with a bunch of other ions mixed in with it. Because this randomness is something the universe likes, the solution will prefer to stay random rather than solidify and become ordered.
Now, this opposition to freezing can only be overcome when enough energy is taken away from the liquid and it simply doesn't have enough energy to stay liquid. Water, for example, stays a liquid until it is cooled to zero degrees Celsius, at which point it starts to freeze. However, if we have a solution that's more random than pure water (such as salt water), its randomness will tend to oppose the tendency to crystallize. As a result, you'll need to take away more energy before the solution will freeze. Lower energy = lower temperature.
The same thing happens to make solutions boil at higher temperatures than pure solvents. A pure solution has some amount of entropy that reflects its disorder. As a result of wanting to become more random, some of the molecules in the liquid will want to become gases - when they form a gas, it results in the formation of vapor pressure. However, if we dissolve something in water, the vapor pressure decreases because the inherent randomness of the solution increases simply by adding the solute. Because the solution has enhanced entropy when compared to the pure solvent, the molecules have less incentive to enter the vapor phase, thus, lowering the vapor pressure at any given temperature. Because the vapor pressure needs to increase to atmospheric pressure before a solution will boil, the addition of a solute raises the boiling point.
Some people used to think that the colligative properties of boiling point increase and melting point decrease were a result of interactions between the solvent and solute molecules. However, studies have shown that even for ideal solutions (where there's no heat of mixing), this lowering of melting point and increase of boiling point would still take place. It's all about randomness!