A database, in the abstract, is:

• A safe place to put an arbitrarily large number of arbitrarily small pieces of information,
• that often encodes relationships between said pieces of information,
• and often encapsulates operations over said information,
• and always includes some sort of storage/retrieval protocol.

The economics of this structure—a large number of small things, arbitrary relationships between them, and bulk operations over them—elicits, if not demands, the use of a computer.