Three  meanings:

First, in copyright law in certain circumstances the term of copyright is measured from the date of first publication – which has a tight definition – the offering or distribution of copies or phonorecords of a work to the public, generally fixed in a tangible medium.  Mere public performance or display of a work does not of itself constitute publication ;

Second, in patent law a publication (i.e., a publicly available description) is typically is usually required to show prior art – there has been an enormous amount of litigation as to what type of public availability qualifies as a publication beyond journal articles and books.  The issue is highly fact specific and can include questions of whether the publication is in an index, in open shelving in a library, etc.  It is not an easy question.; and

Third, with limited exceptions and some grace periods  (e.g., 1 year in the U.S., six months in Japan), publishing an invention before filing for a patent loses the inventor the right to a patent.

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