The title refers to the larger-than-normal orchestra Nelson Riddle gathered for this recording; it is not a documentation of a live performance. This was Frank Sinatra's most fulfilling album of his early Reprise career. It was allegedly Nelson Riddle's favorite Reprise album and was originally recorded on 35mm tape.
Some quotes from my personal Sinatra bible, Sinatra! The Song Is You: A Singer's Art, by Will Friedwald:
Sinatra finds new ways to put over very heavy ballads in The Concert Sinatra... (p. 259)
...The Concert Sinatra derives just as much from Sinatra's career-long quest for extended song forms as it does from his partnership with Riddle...Concert goes for the most high-browed works they can transform into ambitious "concert" arrangements. Concert also represents the closest Sinatra would come to a composer "songbook" album...All but one (Kurt Weill's "Lost in the Stars") of its eight extended selections derive from Richard Rodgers and/or Oscar Hammerstein. (pp. 260, 261)
If the 1956 Close to You represented Sinatra and Riddle at their most intimate, Concert Sinatra finds them at their most epic. Where Close utilizes a chamber group, Concert deploys a complete symphonic contingent. (p. 261)