What is the section of concerto played by a soloist without being supported by an orchestra called?

In music, it is a cadenza that is, generically, an improvised or written-out ornamental passage played or sung by a soloist or soloists without being supported by an orchestra. A cadenza is usually in a "free" rhythmic style, and it often allows for virtuosic display. During the cadenza, it is a time when the accompaniment will rest, or sustain a single note or chord.

With most classical cadenzas, musical experts have noted that the orchestra will come to a sudden halt and the soloist will take flight with a couple of minutes of difficult (or at least difficult-sounding) passage-work interspersed with fragments of melody derived from what has been previously heard. This music usually culminates in an extended trill, after which the orchestra re-enters, bringing the movement to a speedy conclusion, more often than not without any further participation from the soloist.

Noting a list of some of the greatest cadenzas ever played to form musical arrangements, it will normally include: Beethoven's cadenza for Mozart's Piano Concerto No. 20; Joachim's cadenza for Brahms; Kreisler's Beethoven solo; Shostakovich's Cello Concerto No. 1; Prokofiev's Piano Concerto No. 2; Bach's Brandenburg Concerto No. 5; Mozart's Flute Concerto cadenza penned by the Finnish composer Kalevi Aho, and Mozart's Piano cadenza from the prog-jazz pianist Keith Jarrett.