The tray is the part of the jewel box that holds the CD in place. It has a wide spine and is on the right hand side as you open a CD case. Usually, the CD is held in place by a raised round piece in the center (this piece sometimes has teeth) which fits into the hole in the center of the CD. Sometimes trays can be popped out of the jewel cases, but in the case of digipacks, the tray is often glued to the paper backing and cannot be removed without ripping the case.
Trays are typically made of black or clear plastic. The black plastic trays are stronger and hold up better over time, but the clear plastic trays allow artwork to show through when the CD is removed. Trays are also sometimes made of tinted plastic in a variety of colors - colored trays are made of the same thinner plastic as clear plastic CD trays, so they crack easier than the black plastic trays. Clear and colored trays are usually slightly more expensive than the traditional black trays. You can learn more about CD packaging here: