Basically your ODBC driivers (used for database storage) are out of date or corrupt and avast uses ODBC method of database storage.
First check out this avast! FAQ answer http://www.avast.com/eng/other_questions.html#idt_1406. For avast! Pro users it is best to update the ODBC Drivers, Home users can switch to XML storage.
Right click the avast! icon and select Program Settings, then Troubleshooting and tick the Use XML storage instead of ODBC.
You can manually edit the avast4.ini file (using a text editor) and change database=odbc to database=xml, this is in the [Common] section.