Improvisation
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Improvisation is a when a performer is "making it up he/she goes along". In music, one alters what is being played and deviates from the written music. This is done most often in jazz. In an ensemble, the saxaphone, for example, might add trills, extra notes that would complement the melody (called harmony), or even change the key.
Musical Improvisation originated from the African American musicians in the 19th centery. Most were not formelly educated, and they didn't learn music theory. They would sing in church, and they didn't have music sheets written so they had to make it up. As long as it sounded good all together they went for it. Thus they became very talanted and had a good musical ear.