In RC modeling parlance, an "analog" servo uses an older technology analog servo amplifier (amplifier = controller in this terminology).  A "digital" servo uses a servo amplifier with a microprocessor in it.  Digital servos tend to have more torque and shorter response times for the same motor and mechanical assembly.

(Note that there's no fundamental reason you couldn't build a super-hot *analog* controller; it was just never done, and would have been much harder to stuff inside an RC servo case, so the world had to wait for itty bitty microprocessors).