From the manual:
BASE_PERIOD = 50000 - This is the "Base" task period (in HAL), in nanoseconds. This is the fastest thread in the machine.
Note
On servo-based systems, there is generally no reason for BASE_PERIOD to be smaller than SERVO_PERIOD. On machines with software step generation, the BASE_PERIOD determines the maximum number of steps per second. In the absence of long step length and step space requirements, the absolute maximum step rate is one step per BASE_PERIOD. Thus, the BASE_PERIOD shown above gives an absolute maximum step rate of 20,000 steps per second. 50,000 ns (50 us) is a fairly conservative value. The smallest usable value is related to the Latency Test result, the necessary step length, and the processor speed. Choosing a BASE_PERIOD that is too low can lead to the "Unexpected real time delay" message, lockups, or spontaneous reboots.
SERVO_PERIOD = 1000000 - This is the "Servo" task period (in HAL), in nanoseconds. This value will be rounded to an integer multiple of BASE_PERIOD. This value is used even on systems based on stepper motors.
This is the rate at which new motor positions are computed, following error is checked, PID output values are updated, and so on. Most systems will not need to change this value. It is the update rate of the low level motion planner.
TRAJ_PERIOD = 100000 - This is the "Trajectory Planner" task period (in HAL), in nanoseconds. This value will be rounded to an integer multiple of SERVO_PERIOD. Except for machines with unusual kinematics (e.g., hexapods) there is no reason to make this value larger than SERVO_PERIOD.
With a hardware card like the Mesa 5i20 the most import one is the SERVO thread as you probably don't need the BASE thread as the 5i20 is doing the fast work.
Lowering the servo period will make the calculations happen more often and allow less time for non realtime programs (eg EMC's screen controls)
calculating more often make the system more responsive to feedback. I believe its called bandwidth .
For most servo systems with velocity amplifiers, the 1KHz (1000000ns) period is recommend.
If using torque controlling amps, linear motors, or motor commutation with EMC for instance I have seen 5 KHz (200000ns) recommended
I'm sure someone more knowledgeable will add to this but what would help the most is:
What are you trying to improve?