The SN2 reaction favors slightly less polar aprotic solvents such as (acetone, acetonitrile, DMF). A very polar protic sovent will decrease the reactivity of you nucleophile by tieing up (solvating) the nucleophile. Thd following illustrates the interaction of water a polar protic (wrong solvent for SN2!) with NaBr. You don't want the Br- to be heavily solvated.
On the other hand a less polar aprotic solvent such as acetonitrile would not solvate the Br-. This is considered a ground state effect.