DOI's are required (if available) if you use APA style, and are valuable tools for your Zotero library (EndNote, Mendelay, and other reference management sopftware applications as well, I believe) as you can paste in a DOI and have it automatically create a bibliographic record for the article/dataset/chapter/whatever. DOIs can also be an important tool for alternative methods of promoting and determining the spread and impact of scholarly work ("altmetrics") because they provide a common reference link. and you can search by them to get to the article/chapter/etc.
CrossRef is Crossref is "an official Digital Object Identifier Registration Agency of the International DOI Foundation" and manages most academic journal DOIs: "Crossref makes research outputs easy to find, cite, link, assess, and reuse. We’re a not-for-profit membership organization that exists to make scholarly communications better."
DOI example: 10.1186/s13059-014-0424-0 (they can be longer or shorter, and include letters)
Page link: https://libguides.libraries.wsu.edu/zotero/doi