Well, the article here:
http://en.wikipedia.org/wiki/Spherical_robot is surprisingly sparse, but is is essentially correct.
Most spherical robots consisted of 3 axes -- 2 rotational, and 1 linear/prismatic.
Imagine a pan/tilt camera mount, or a gun turret, or an alt/azimuth telescope. That is what the first two axes would be like.
The third axis, the linear/prismatic axis, would essentially be a "telescoping" axis, extending and retracting the reach of the robot's gripper or other tooling. So the robot's work envelope would be defined as a hollow sphere, with the inner radius defined by the shortest possible extension of the linear axis, and the outer radius defined by the furthest extension of the linear axis. The hollow sphere would also be incomplete, due to the first two (rotational) axes not being free to rotate a complete 360deg.