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Method 1:
Go to Menu > Settings > Application > Manage Applications> Play Store.
Therein, you can see the Clear Cache, and Clear Data options. Click on both of them respectively.
Head back to the home, and reboot your phone.
Try downloading or updating apps from google play store. The error 101 problem has most probably been solved by now, but in case the error still occurs while downloading, for the final process you will be required to remove your Google account and add it again.
Method 2:
Go to Menu > Settings > Accounts & Sync
Select Google account > Click menu >> Select Remove Google
Add your Google account again.
Now try downloading the app from the play store. The error 101 has been most probably solved by now.