A clock with a second hand that jumps once per second, then there is almost certainly a tiny permanent magnet stepper motor inside the mechanism, which turns 180 degrees once per second. The timekeeping is done by a 32 kHz quartz crystal, divided to produce a one-time pulse per second. The stepper motor's field coil receives a brief current pulse every second, which causes the armature to move half a turn before stopping.
The motor's magnetic circuit is set up so that its armature will halt in one of two positions that are 180 degrees apart, with the poles of the permanent magnet rotor near the iron poles of the field. The drive current pulses alternate in polarity (positive or negative), so each pulse pushes the motor to turn 180 degrees. The motor drives the second hand through a 30:1 reduction gear, and the minutes and hours hand is driven mechanically from the second hand.
Other arrangements are possible too. I have a Seiko desk clock that is battery-powered and seems to move the second hand continuously. It might be moving in discrete steps 8 or 16 times per second instead of once per second, or the motor could rotate continuously. The time signal is provided by a quartz crystal, regardless of the driving technique employed. This clock requires more power than a clock that only moves once every second because it runs on a "C" battery as opposed to an AA.
Some clocks have no second hand. These may be built so that the hands only move once every 20 seconds to reduce power consumption. If you listen to the mechanism of a clock, you can probably determine if it advances once per second or once every twenty seconds.