A Cadenza is a parenthetic flourish in a solo piece commonly used just before a final or otherwise important cadence. In a concerto, a cadenza will often have the orchestra stop playing while the soloist performs alone. While cadenzas were originally improvised, modern music typically writes out the cadenza portion.
Beethoven's "Emporor" Concerto
Aaron Copland's Clarinet Concerto
Tartini's "Devil's Trill" Sonata
The First cadenza that was published was composed by Wolfgang Amadeus Mozart.