Jasper beads are made of small quartz crystals, specifically chalcedony.
There are many names applied to jasper, as the names often refer to the origin of a particular pattern or color. In the case of brecciated jasper, opal is the cementing material that holds fragments of jasper together.
It is generally opaque and has some pattern to it, but comes in all colors. If heavily banded, jasper is called an agate. Jasper jewelry components are especially desireable, due to jasper's wonderful array of colors and exceptional durability. It is not easily fractured or scuffed.