It's a concept that is rooted in entropy.
The term colligative property does not take into account the intermolecular forces/interactions involved.
Essentially, you can compare this to an ideal gas; the same principles apply.
The easiest example is that of vapor pressure lowering. Why does this happen when a solute is added to a pure liquid?
We start by asking what the tendency for vaporization is. The tendency for a liquid to vaporize is due to the gain in entropy; the entropy change for a liquid vaporizing is positive. Now ask...what is the contribution of enthalpy? The change in enthalpy for vaporization is equal to or greater than zero....
Now, when you add a solute, there is generally a gain in entropy. The "initial" state is higher in entropy than the initial state of a pure liquid.
Thus, a solution is accompanied by a lower change in entropy following vaporization; for the sake of simplicity, you may assume the final state to be the same in terms of absolute entropy.
Because the change in entropy is smaller, the tendency to vaporize is lower. This corresponds to a lower gibbs free energy which is related to a lower equilibrium pressure.
Think in terms of entropy with respect to osmotic pressure and it should be a bit more clear.
Freezing point depression also can be explained in terms of entropy as well, but I don't know how to do it w/o drawing a graph. It helps to understand that the melting point is when the vapor pressure of the liquid phase and solid phase are equal...
Unless you're willing to consult a physical chemistry textbook, the underlying principles of colligative properties cannot be fully explained...many gchem books shy away from it as well.
For the DAT it's probably in your best interest to just remember the general rules:
Boiling point elevation when you add a solute; also accompanied by freezing point depression, etc.
Being familiar with the principles of fractional distillation (ie when a volatile solute is added) is also a good idea.
