${\text{BeF}}_2$ has zero dipole moment, whereas ${\text{H}}_2\text{O}$ has a dipole moment because 

The geometry of  ${\text{BeF}}_2$ molecule is linear and the hybridization is sp. In ${\text{BeF}}_2$ molecule, both the dipoles act in opposite directions by bond angle $\text{180}°$. So, the net dipole moment is zero. Water molecule has a net dipole moment this is because the geometry of water molecule is bent or angular with the bond angle $104.5°$.Hence, the dipoles acts in water are not cancelled out like ${\text{BeF}}_2$.  Let us see the diagrams in the below.