If you want other computers that are connected to your Home Sharing to be able to play the movies, music and apps that you have downloaded from the iTunes store, you must authorize each of them. This is particularly important for music bought before the "DRM free"--without copy protection--purchase option.
To authorize the other computers: Click on "store" in the top menu, then choose "authorize computer." Enter the iTunes user name and password to authorize the computer to play the songs bought by that user. You must authorize each computer with each iTunes user whose content you want to play. A family may need to authorize for the mom's, dad's and son's account, and so on. Now everyone can play each other's purchased movies and music.