The dipole moment of any molecule is the vector sum total of each of the dipole moments. In BCl3 molecule, although the B–Cl bonds individually are polar, the resultant dipole moment becomes zero. We can see that the dipole moments of $\mathrm{B}\overset{1}{-}\mathrm{Cl}$ and $\mathrm{B}\overset{2}{-}\mathrm{Cl}$ produce a resultant which is equal in magnitude but oppositein direction to $\mathrm{B}\overset{3}{-}\mathrm{Cl}$ and hence cancels it out. That is why the net dipolemoment of $\mathrm{BCl}_3$ is zero.