“ellipsis: The omission of one or more elements from a construction, especially when they are supplied by the context. E.g. if A asks Have you seen my glasses? B might answer eliptically I’m afraid I haven’t, with the remainder of the construction (seen your glasses) to be understood from the question. Hence ‘to ellipt’: thus seen your glasses would be ‘ellipted’ in B’s answer.
Also, in some usage, whenever a null element is posited. E.g. in I am afraid [he left], a subordinate clause (in brackets) might be said to begin with a null complementizer, representing an ‘ellipsis’ of the overt complementizer in I am afraid [that he left]. The way the term is applied may also depend in part on where words are described as pro-forms. Thus in John DID, with emphasis on did, one might say that a part of the construction is missing: compare John DID see them. Therefore there is no ellipsis. But where the stress is on John, one might be tempted to argue that there is no ellipsis: JOHN did, but not, with a similar expansion, JOHN did see them. Instead did might be described as a pro-form which completes the sentence on its own.
Excerpted from: Matthews, P.H., ed. The Oxford Concise Dictionary of Linguistics. New York: Oxford University Press, 2014.