MARC 21 format for Bibliographic Data is a standard designed to be a carrier for bibliographic information about printed and manuscript textual materials, computer files, maps, music, continuing resources, visual materials and mixed materials. Bibliographic data commonly includes titles, names, subjects, notes, publication data and information about the physical description of an item. The standard defines formats for the representation and exchange of bibliographic, authority, holdings, classification and community information data in machine-readable form.
A MARC record is composed of three elements:
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Record structure: an implementation of the international standard Format for Information Exchange (ISO 2709) and its American counterpart, Bibliographic Information Interchange (ANSI/NISO Z39.2).
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Content designation: the codes and conventions established explicitly to identify and further characterize the data elements within a record.
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Data content of the record: the content of the data elements that comprise a MARC record is usually defined by standards outside the format (e.g. ISBD, AACR2, RDA).
The MARC 21 standard also provides lists of source codes for vocabularies, rules and schemes.
The MARC 21 standard is maintained by the The Network Development and MARC Standards Office and documented in detail: https://www.loc.gov/marc/marcdocz.html.
For a short introduction to MARC 21 see the OCLCs "Introduction" or "Understanding MARC Bibliographic: Machine-Readable Cataloging" for a more detailed one. The history of MARC is documented in "MARC, its history and implications".