Performing music from memory
Although some people can learn music by ear, most people who are taught to play musical instruments learn new pieces by reading the printed music which is in front of them on a music stand.  When someone has learned to play a piece of music well enough to perform it, it is good if they can learn to play it without the printed music.  This is called “playing from memory” or “playing by heart”.  When a musician is practising a piece of music so that it can be played from memory this is called memorizing the music.