Answer
The curved arrows in the picture show the movement of electrons. $H_2O$ is the Lewis base (nucleophile) and ${(CH_3)}_3O^+$ is the Lewis acid (electrophile).
Work Step by Step
The lone pairs on water attack the C, and then since C now has more than 4 bonds, the bond between the $CH_3$ and O breaks and the electrons go to O, forming $CH_3-O-CH_3$ ion. Since $H_2O$ donates a pair of electrons it is lewis base and ${(CH_3)}_3O^+$ accepts a pair so it is lewis acid.
