The word cadenza denotes a complicated thing. At the end of a movement in a concerto—which is, as you know, an extended piece for a featured soloist and orchestra, usually in three movements—there often is a big chord, after which the orchestra players lay down their instruments, and the soloist plays an entire virtuoso passage, usually touching on the themes of the preceding movement. This is a cadenza. The exciting part, for me anyway, is how they smoothly flow into the last few chords of the movement, and end it.
In the old days of Vivaldi and guys, the cadenzas were improvised by the soloist. More recently, the composer wrote out a cadenza for the soloist. Modern soloists are eager to go back to the improvised cadenza!
Just the other day, I was listening to Joshua Bell playing the Mendelssohn violin concerto, (his only one). But, JB played his own cadenza! Oh, I missed Mendelssohn's own cadenza so much!! It's a fun cadenza, but I guess musicians are bored with it; same old, same old, they think. I first heard this piece when I was just about 14 or 15 years old, and got to know and love Mendelssohn's cadenza... oh man; that's really too bad. I'll just go off and cry by myself, now...
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