Polar aprotic solvents are very effective in solvating cations, but not nearly so effective in solvating anions. Because anions are only poorly solvated, they participate readily in SN reactions, and nucleophilicity parallels basicity: F- > Cl- > Br- > I-
Polar protic solvents anions are highly solvated by hydrogen bonding with the solvent the more concentrated the negative charge of the anion, the more tightly it is held in a solvent shell the nucleophile must be at least partially removed from its solvent shell to participate in SN reactions because F- is most tightly solvated and I- the least, nucleophilicity is I- > Br- > Cl- > F-