This question might be better answered by taking a look in the product documentation or product brochures for Visual COBOL. There is a link to the Product Documentation from this page.
A brief description would be:
Visual COBOL supports standard and extended COBOL file handling I-O statements such as OPEN, READ, WRITE, REWRITE, DELETE, etc against file types such as record sequential, line sequential, indexed and relative files. Fileshare is also available allowing you to process data files across a network. Many different file formats are supported.
Visual COBOL supports a number of database preprocessors to provide support for embedded SQL statements using EXEC SQL/END-EXEC. This includes MF OpenESQL (ODBC, ADO, JDBC), Oracle Pro*COBOL and DB2 preprocessors.
Visual COBOL also supports a component known as DB Connectors which allows you to use COBOL I-O statements to access database tables.
Visual COBOL also supports a component known as Relativity that allows you to access COBOL data files thru an ODBC connection.
Your question about batch and on-line programs leads me to believe that you might be coming from a mainframe environment. Visual COBOL is for developing non-mainframe applications that will run across distributed platforms such as Windows, Linux or Unix. If you have mainframe applications that use CICS or IMS, JCL etc. then the product you should be looking at would be Enterprise Developer which supports running both batch and on-line CICS applications under a product called Enterprise Server.
If you have any specific questions please feel free to ask.