An identifier is a name that you assign to a data object. It can be a word, number, letter, symbol, or any combination of those. Ideally, the identifier is unique within your identifier system. A "persistent identifier" is an identifier that is available and managed over time; it will not change if the item is moved or renamed. This means that an item can be reliably referenced for future access by humans and software. Services can provide you with unique, persistent identifiers that you can apply to your data object and manage it over time.
An ARK , or archival resource key, is a URL with extra features allowing you to ask for descriptive and archival metadata and to recognize certain kinds of relationships between identifiers. ARKs are used by memory organizations such as libraries, archives, and museums. ARKs are appropriate for descriptive metadata, or data sets in active development, for which you want a consistent ID but whose content is likely to evolve over time.
A DOI, or Digital Object Identifier, is a popular type of identifier that is guaranteed to be unique. DOI's have been used for several years for published material that isn't going to change, and increasingly they are being used for final data sets as well. If you revise something with a DOI, the revision should get a new DOI.