[Super Newb]

It has been generally accepted that aprotic solvent is the best solvent condition for Sn2 reaction due to its ability to solvate the cation but leaving the nucleophile unencumbered. Polar aprotic solvents (e.g., DMSO, acetone, acetonitrile, DMF) are very effective in solvating cations, but not nearly so effective in solvating anions. Why is that so?

[AdiDex]

As far as I know Solvation occurs better if charge density on solvent is high . If solvent has localized positive charge then it will solvate Anionic substrate , If Solvent has localized Negative charge then it will solvate cationic substrate . If it has localized positive as well as negative charge  then it will solvate both cationic and anionic parts.

Lets take an example of NaBr in H₂O .
It has good enough negative charge density in Oxygen's region so It will interact strongly with Na⁺ . Although the positive charge in Hydrogen region will be lower than Oxygen but due to having very small size , The charge density become very high (Since Charge Density = Charge / Size ) so it will interact strongly with Br^- also .

now take an example of CH₃OK in DMSO ,
DMSO has only negative localized charge on Oxygen region but it has dispersed charge on 2 Methyl region . SO it will solvate the K⁺ only .

[Babcock_Hall]

It has been generally accepted that aprotic solvent is the best solvent condition for Sn2 reaction due to its ability to solvate the cation but leaving the nucleophile unencumbered. Polar aprotic solvents (e.g., DMSO, acetone, acetonitrile, DMF) are very effective in solvating cations, but not nearly so effective in solvating anions. Why is that so?

Super Newb,

According to the Forum Rules, you must give your thoughts before we can help you.  I would also point out that there are different classes of S_N2 reactions based upon whether or not the nucleophile is charged, and whether or not the leaving group is charged.