Archives are collections of historically important material that are organized and made accessible to preserve information on individuals and organizations. These materials provide evidence of the day-to-day activities of the people and organizations which originally created the collections. Materials considered "archival" could be, but are not limited to, photographs, correspondence, minutes, maps, audio-visual material, and publications.
Archives and Records Management: Bibliographies, Web Links and Professional Organizations
Mark Greene, “Access to Institutional Archives and Manuscript Collections in U.S. Colleges and Universities,” http://www.archivists.org/publications/proceedings/accesstoarchives/08_Mark_GREENE.pdf
Society of American Archivists, North America's oldest and largest national archival professional association.
Using Archives: A Guide to Effective Research
Typically you would see a box like this if it was an unprocessed, or disorganized, collection. These boxes are called either Records Cartons or Paige Boxes.
More likely you will see something like this, which is called a Manuscript Box.