.BDB files are backups of .WDB files, database files for Microsoft Works. These files are generated automatically by Works in case the original WDB file becomes corrupt.
Microsoft Works is an office suite available from the Microsoft Corporation. It is considered by most to be a smaller, less expensive version of the Microsoft Office suite; it includes the Microsoft Works word processor, the Works spreadsheet, and the Works database.
Microsoft's Word is able to open (and save as) Works word processor documents, and Microsoft's Excel is able to open (and save as) Works spreadsheets.