What is molarity and molality?

Molarity is a measure of the concentration in terms of number of moles of solute per liter of solution, having the unit symbol mol/L or mol/dm³ in SI unit.

Molality is also a measure of concentration in terms of number of moles of solute per kilogram of solvent.

The most significant difference between them is that molarity in terms of volume of the solution while molality is in terms of the mass of solvent.

In chemistry, colligative properties include lowering of vapor pressure, elevation of boiling point, depression of freezing point and osmotic pressure.  They are those properties of solutions that depend on the ratio of the number of solute particles to the number of solvent molecules in a solution, and not on the nature of the chemical species present.  Note that the addition of solute does not change the mass of solvent used when molality is used, but the addition of solute does change the volume of the solution to some extent.  Molality can directly describe the ratio of the number of solute particles to the number of solvent molecules in a solution, but not molarity.  Therefore, molality is more suitable to be used in colligative properties.

Molarity: moles of solute per liter of solution
molality: moles of solute per kilogram of solvent

Molarity is temperature dependent because the volume of solutions changes with temperature. Molality is temperature independent.