dexterous workspace
The dexterous workspace of a robot arm is the smaller, choosier region where the hand can not only reach a point, but reach it pointing in any direction you want. In the bigger reachable workspace, the arm can merely touch a spot somehow; in the dexterous workspace it has full freedom of angle there — it can hold a tool upright, tilt it, flip it over, aim it any which way, all while staying at that same location.
This extra demand is strict, so the dexterous workspace is always tucked inside the reachable one, and usually much smaller — often a snug core near the middle of the arm's range, away from the far-out, fully-stretched edges. Out at the fringes the arm can still touch things, but only at one forced, locked-in angle, like reaching a high shelf with your arm dead straight: your fingertips arrive, but you cannot freely rotate your hand once you are there.
This region matters enormously for tasks that care about orientation, not just position — screwing in a bolt, pouring from a bottle, welding a seam, guiding a surgical tool. For those jobs the workpiece must sit inside the dexterous workspace, because being merely reachable is not enough; the hand has to be able to face it the right way too.
Hold a cup of water near the center of your reach and you can freely tilt it to any angle on command. Now hold it at full arm's stretch: you can keep it level, but you can no longer roll your wrist around freely. The near zone is your dexterous workspace; the far edge is reachable but not dexterous.
Near the body you can freely re-aim the cup (dexterous); at full stretch you can reach but not freely rotate.
Many simple arms have a very small dexterous workspace, or none at all, even though their reachable workspace is large.