A term in
Classical Music. A Cadenza is an unaccompanied solo in the middle of a piece written (otherwise) for that instrument with accompaniment. It's also a chance for the soloist to demonstrate their skills on their instrument; in this regard the Cadenza can be likened to an 80's
guitar solo (characterized by
shredding, or very fast,
virtuosic playing). Cadenzas are found most often in
concertos, although they can be in any piece with a soloist.
Up until the early 19th century, cadenzas were often improvised by the performer, rather than written into the music. During the Romantic era, it became the norm to write out the cadenza. In fact, many cadenzas were written by notable Romantic composers (such as Liszt and Schumann) for concertos by classical (18th century) composers such as Beethoven and Mozart. These written cadenzas have now become the standard cadenzas played, but occasionally a performer will improvise his/her cadenza today in pieces where the cadenza wasn't originally written. When the cadenzas were/are improvised, there was no specified length - the performer simply played until he/she was done, at which point a trill was the usual signal for the orchestra to jump back in.
For an example of a cadenza, listen to Tchaikovsky's first Piano Concerto. Right after the introductory theme is introduced, there is a small cadenza, the first of several in the piece, in which the orchestra stops and the soloist performs some terrifying musical feats on the piano (in this one, huge arpeggios). Or, Tchaikovsky's Violin Concerto in D. There the Cadenza happens quite a ways through the piece (I can't remember how far into it exactly). The violin is heard solo, once again running through some staggering arpeggios, skips, double stops, etc, after which you can hear the traditional long trill, at which point the soloist is joined by the orchestra again (although, with a written cadenza there is no need for a trill to signal the conductor, as in the cadenza I mentioned first).
Of course a cadenza is not just about technicality. In classical music more than any other style (except perhaps metal or progressive rock), musicians with incredible virtuosity are a dime a dozen; what really matters is expressiveness on the instrument. In this regard, the cadenza is perfect because it combines the amazing depth of classical music, in both complexity and emotive capability, with truly impressive technicality.