The number of moles of solute dissolved in $1\text{kg}$ of a solvent is defined as:

Molality ($m$) is defined as the concentration of a solution expressed as the number of moles of solute per kilogram of solvent:
$$m=\frac{\text{Moles of solute}}{\text{Mass of solvent in kg}}$$

Molarity, on the other hand, measures moles per liter of solution.