Polar protic solvents:
Stabilize the carbocation intermediate. A polar protic solvent, such as methanol, has a permanent dipole which means that the delta negative (partial negative charge) on the molecule will have dipole-dipole interactions with the carbocation, stabilizing it.
Reduce the reactivity of the nucleophile. The polar protic solvent can interact electrostatically with the nucleophile thereby stabilizing it. This reduces the reactivity of the nucleophile which favors an Sn1 reaction over an Sn2 reaction.
A polar protic solvent stabilizes the Sn1 intermediate and reduces the effectiveness of the nucleophile which favors Sn1 reactivity over Sn2 reactivity.