Freestyle rap (also known as battle rap, battle rapping or battle rhyming) commonly refers to rap lyrics which are improvised through an a cappella or with instrumental beats, i.e. performed with no previously composed lyrics, or "off the top of the head." Nicki Minaj rose to fame primarily as a rapper, and did several of such freestyles throughout her career.
Freestyling may also refer to rapping over another artist's instrumental, not necessarily improvising. This category includes only Nicki Minaj's improvised raps; for Minaj's raps over others' beats, see covers.