The Digital Object Identifier (DOI) is a unique identifier used to provide a permanent link to digital objects. DOIs are now issued to most (new) journal articles, as well as many books, book chapters, and other items.
Several professional association style guides now specify the use of the DOI when citing journal articles. For example, APA recommends the use of the DOI over the URL. Many publishers also request that the DOI be included in submitted manuscripts, even if they are not included in the final published paper, as they use them for formatting and to link references with electronic databases.
In general, if a CSL/Zotero style includes the DOI, it is a good idea to leave it in. If you have a good reason to remove the DOI from the official style, it is possible to edit the CSL style. See this discussion for more details.