A jewel case is the plastic case that holds CDs. "Jewel" refers to the piece that clips into the center hole of the CD to keep it in place. It has a jewel-like design. It is just a clever name for a CD case. They are the slimmer version of the standard CD case. They are made up of a front cover that pivots open to the left (as you are holding the CD), a back cover and a tray that sits in the back cover which holds the CD. The front cover artwork is held in the front cover part of the jewel case - this is the booklet with photos, liner notes, lyrics and such - and the back cover holds the tray card, which usually has the track listing and other artwork on the back side that can be viewed with the CD closed and may have other artwork on the front side that is visible when the CD is removed from the tray.
Jewel cases are usually made of clear plastic, although they are sometimes made of tinted plastic that is still transparent. The tray part of the jewel case is sometimes made of black plastic and sometimes made of clear/colored plastic. The black plastic trays are heavier and stronger than the other, thin plastic used to make the rest of the jewel case, but sometimes the thinner clear/colored options are chosen for the tray for aesthetic reasons.