A translucent rock or mineral is one which allows some light to pass through but is not completely transparent. It may not always be immediately apparent whether a stone is translucent and it's easy to be fooled into thinking it's opaque. By holding a stone up to a bright source of light you'll see immediately whether any part of it is translucent. It's not unusual in some stones for only a small area to exhibit translucency.
Gemstone varieties which exhibit a good degree of translucency are usually faceted because the cuts in the stone emphasize the way in which it interacts with light and therefore also help to enhance its colour. Most of the world's finest gemstones are faceted in order to maximise their beauty.