Overt means ‘manifest, apparent, visible’ as opposed to covert ‘hidden under the surface’. The distinction was introduced by B.L. Whorf (1956) with reference to grammatical meanings which may either be coded by segmental means, i.e. by morphemes, morphological processes or words conveying the grammatical meaning in question, or may just be a semantic aspect of a syntactic construction without having an expression of their own. An example is the alienability distinction, which is expressed by a morphological opposition in languages like Yucatec Maya, but only signalled indirectly at the syntactic level by the admissibility of certain constructions for either alienable or inalienable relations in languages like English.

The distinction between ‘overt’ and ‘covert’ is reasonable for semantic entities, esp. grammatical meanings. It makes no sense for expression entities including features of linguistic structure, as these are by definition overt. Expressions like overt ending or overtly marked – not seldom encountered in linguistic publications – are thus just pleonastic for ending and marked. Likewise, an “overt morpheme” makes sense only if opposed to a zero morpheme (a morpheme without a significans being rather similar to a grammatical meaning); otherwise it is just a morpheme.

In certain varieties of generative grammar, a distinction is made between two levels of grammatical structure, one called ‘surface structure’ and corresponding to other linguists' ‘grammatical structure’ and another called ‘underlying structure’ (or other more or less suggestive names) and corresponding to nothing in the rest of linguistics. In such approaches, much of grammatical terminology has been redefined as here illustrated by the example of ‘case’:

This is an important contribution to confusion in scientific terminology.

Reference

Whorf, Benjamin L. 1956, Language, thought and reality. Selected writings, ed. by John B. Carroll. New York: J. Wiley.