Answer
The curved arrows in the picture show the movement of electrons. $CH_3O^-$ is the Lewis base (nucleophile) and $CH_3Cl$ is the Lewis acid (electrophile).
Work Step by Step
The lone pairs on Oxygen attack the C, and then since C now has more than 4 bonds, the bond between the $CH_3$ and $Cl^-$ breaks and the electrons go to Cl, forming $Cl^-$ ion. Since $CH_3O^-$ donates a pair of electrons it is lewis base and $CH_3Cl$ accepts a pair so it is lewis acid.
