Step 1: Water's hydrogen-bond network must be disrupted.
Pure water molecules are linked by strong O-H...O hydrogen bonds. Dissolving any solute requires breaking some of these bonds, which costs significant energy.
Step 2: Alkyl halides cannot form compensating H-bonds.
Although the C-X bond in R-X is polar (due to the electronegative halogen), alkyl halides have no O-H or N-H groups. They CANNOT form hydrogen bonds with water. The only possible interaction is weak dipole-dipole or van der Waals forces between R-X and $\text{H}_2\text{O}$.
Step 3: Unfavourable energy balance causes low solubility.
Energy released by weak R-X...water interactions is far less than the energy required to break strong O-H...O hydrogen bonds in water. Net dissolution is energetically unfavourable. Despite being polar, alkyl halides are therefore sparingly soluble in water.