Field: A single piece of information about an object. If the object were an Employee, a field would be Firstname, Lastname, or City or State.
Record: A collection of fields. In an Employee file, there would be one record for John Smith, another record for Mary Jones, and another record for Al Newman.
File: A collection of bytes. The bytes may represent numbers or characters. In business systems, files usually consist of collections of records. In this drawing, each filecabinet drawer represents one file. Here's a simple definition.
Index: Similar to a library's card catalog: in a library it provides quick access to a particular book; in a computer, an index provides quick access to a particular record within the file that it indexes.
Database: This word is frequently mis-used, but one definition would be a collection of indexed files. Relational databases contain relations between the files' records. For example, a shop might have a file of Employee records and a file of Vendor records and a file of Purchase Order records. Each purchase order record will contain a Vendor number and an Employee number for the employee who created the purchase order. If there are five purchase orders for one vendor, each of those five purchase orders will be related to a single record within the Vendors file. When you view or print a purchase order, it will contain information from the Purchase order record, as well as information from the related Vendor and Employee records.