Meaning Freshly printed. Origin This term is applied especially to newspapers.
Newsprint presses generate heat when printing, by a process called, for obvious reasons, 'hot metal printing'. Although the term only really makes complete sense for things like newspapers which are pressed and hot, it is by extension now also used to refer to anything that is fresh and newly made.
Hot off (or from) the press (or presses) didn't originate as a phrase until the middle of the 20th century. For example, The Times August 1955: "But it is for novelties, hot from the press or the copyist's desk, that discontent is calling." The hotness is a clear allusion to the hot metal process, but may also allude to an earlier usage of hot news , i.e.

to mean striking or sensational news. This is used in a Daily Express story in September 1914: lanciao 'Hot news' ... must be provided for the people, and thus we learn from the Vienna 'Abendblatt' that General French is a prisoner.