DOI is:
In computing, a Digital Object Identifier or DOI is a persistent identifier or handle used to identify objects uniquely, standardized by the International Organization for Standardization (ISO). An implementation of the Handle System, DOIs are in wide use mainly to identify academic, professional, and government information, such as journal articles, research reports and data sets, and official publications though they also have been used to identify other types of information resources, such as commercial videos.
A DOI aims to be "resolvable", usually to some form of access to the information object to which the DOI refers. This is achieved by binding the DOI to metadata about the object, such as a URL, indicating where the object can be found. Thus, by being actionable and interoperable, a DOI differs from identifiers such as ISBNs and ISRCs which aim only to identify their referents uniquely. The DOI system uses the indecs Content Model for representing metadata.
The DOI for a document remains fixed over the lifetime of the document, whereas its location and other metadata may change. Referring to an online document by its DOI is supposed to provide a more stable link than simply using its URL. But every time a URL changes, the publisher has to update the metadata for the DOI to link to the new URL. It is the publisher's responsibility to update the DOI database. If they fail to do so, the DOI resolves to a dead link leaving the DOI useless.
http://www.doi.org/ is the website of the International DOI Foundation. This website resolves a DOI into an URL.