A Digital Object Identifier or DOI is a persistent identifier or handle used to uniquely identify objects.
DOIs are often assigned by publishers and repositories. They are used to help identify unique items easily and are used in citing data, articles, etc. Their ease of location contributes to their ease of use / reuse and their usefulness when doing reproducibility studies.
DOIs can also be assigned via the site DOI.org.
"ORCID provides a persistent digital identifier that distinguishes you from every other researcher and; through integration in key research workflows such as manuscript and grant submission; supports automated linkages between you and your professional activities ensuring that your work is recognized" (ORCID.ORG)
Used together with unique identifiers of your research output (DOIs) - which can be added to your ORCID - these identifies enable researchers to:
Used together with any open access publication / data, ORCID and DOIs make it easier for your research to be discovered and used.