A zero article is an unpronounced article present in some languages. Linguists hypothesize the presence of the zero article based on the X-bar theory.
Examples
In a sentence "__ John was lying on the chair" the noun phrase "__ John" is said to have a zero article rather then no article. Compare to "A book was lying on a chair", here the noun phrase "a book" clearly has an article. Thus it is logical to assume that a noun phrase "___ John" should have an article as well.