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.