What is the freezing point depression?
Lowering the freezing point of a substance by adding something (typically the addition of a solute to a liquid).
The easiest way to present this is to think about sea water, which can have a freezing point below that of pure water. This is due to the number of dissolved solutes in the water.
The solidification (freezing) of water is due to the attractive forces of the water molecules overcoming the kinetic energy of those particles. Once that occurs, the water molecules come together in a crystal like structure that we call ice. This happens, under standard conditions, at zero degrees celsius. When these solutes are present, they interrupt the attractive forces between the water molecules, and it allows these particles to continue to move around in the liquid state at temperatures where normally they would have formed ice.
Here is a video which illustrates how to calculate the freezing point depression of water for 1molal solutions of sugar and NaCl.