According to Isaac Asimov's Foundation and Earth, Galaxia is (or will be) a living organism which contains all the lifeforms and rocks and other materials in the galaxy. It is a Utopia, the successor of Gaia (similar being encapsulating only one planet).

One important point should be made about the 'inevitability' of Gaia's transformation into the galaxy-encompassing Galaxia, thus becoming the final evolution of the Second Galactic Empire:

Repeatedly throughout The Foundation Series, short excerpts are given from the "Encyclopedia Galactica" which is an encyclopedia that contains all (or most) human knowledge. The date given for the edition of the Encyclopedia Galactica that these excerpts come from is 1,020 years after the Foundation is founded; during the Second Galactic Empire.

From Foundation's Edge it can be surmised that Galaxia culminates in about FE 4000, allowing for further Foundation stories to be interesting until that date, if the Estate of Isaac Asimov were to authorize further stories. (Vis-a-vis Donald Kingsbury's novel, Psychohistorical Crisis )