Here's the official definition, courtesy of DOI.org:
The Digital Object Identifier (DOI) System is for identifying content objects in the digital environment. DOI® names are assigned to any entity for use on digital networks. They are used to provide current information, including where they (or information about them) can be found on the Internet. Information about a digital object may change over time, including where to find it, but its DOI name will not change.
The DOI System provides a framework for persistent identification, managing intellectual content, managing metadata, linking customers with content suppliers, facilitating electronic commerce, and enabling automated management of media. DOI names can be used for any form of management of any data, whether commercial or non-commercial.
A DOI, or digital object identifier, is like a social security number for a document online. It’s a unique and permanent identifier that will take you straight to a document no matter where it’s located on the Internet. It's a combination of letters, numerals, and punctuation. Journals in psychology, science, nursing, and medicine have been among the earliest adopters of the DOI; some journals in social sciences and humanities use it as well. It's less likely to be used in popular magazines and newspapers. If a DOI is available, you don't have to cite which database the article was found through, or the URL of the journal publisher.
In best publishing practices, the DOI should be listed prominently on the first page of a journal article, whether in print or online. If you’re working online, copy and paste it into your reference list, to avoid transcription errors. Do not alter the alphanumeric DOI string in any way. If you used one of the library's licensed databases (e.g. PsycINFO, Medline, BioOne) the DOI may also be listed in the record that described the article. Here is a short tutorial on locating the DOI: http://blog.apastyle.org/ap astyle/2009/12/how-to-find-a-doi.html
Check the style manual that you're using to note proper placement of the DOI in the reference citation. (e.g., APA, AMA, CSE) Here's a sample reference using APA style 7th edition:
Borman, W. C. (2005). Role of early supervisory experience in supervisor performance. Journal of Applied Psychology, 78, 443-449. http://doi.org/10.1037/0021-9010.78.3.443
If you do not find DOIs for the printed materials that you read, then you do not have to include anything further. You’re done! (Note that many books that exist only in print form are not likely to have DOIs at this time.) When you’ve read something in print form and no DOI exists, simply follow the reference format for print materials.