Firstly, we need to know the characteristic of centrifugal pump or fan. According to the study of centrifugal pump, its characteristics highly depends on the rotation speed. Please refer to the below formula.
Q1/Q2=n1/n2,  flow depends on speed proportionally;
H1/H2=(n1/n2)^2, pump’s head depends on speed proportionally in the second degree;
P1/P2=(n1/n2)^3, shaft power depends on speed proportionally in the third degree;
Here also attached a graph to help you understand the formula well.

When the adjusting method is by valve(throttling),it will lead to much energy loss than using VFD to adjust speed. The pink rectangle part is the power loss in the graph.
When we use a VFD to decrease the pump speed from n1 to n2,you can see than the flow Q and the head H also decreased. Of course, the shaft power also decreased obviously.
In theory, when you no need full water flow, for example 80% water flow you need now, the VFD will decrease the speed to 80%,the shaft power will decrease to 80%^3 which is 51.2%.
When the flow demand decreases to 50%,according to the formula, the power will reduce to 50%^3 which is 12.5%. In actual using, the actual energy savings can not reach to the theoretical value, but the saving rate also reach 20% – 50%.

Advantages of using VFD for pump or fans applications
a. Easy to install and use, power saving rate can be as high as 20% (Normally 20% to 50%).
b.Soft start and stop, avoids strong current and mechanical shock, effectively extend the service life of equipment.
c.Over-voltage, under-voltage, overload and other automatic protection functions to prevent accidental damage to equipment.
d.Manual and automatic energy saving switchover function to ensure the normal operation of the equipment.
e.High power factor output, reduce reactive power loss and compensation capacity, reduce motor heating, extra loss and noise.
f.Improve equipment operating conditions, reduce mechanical wear and repair, maintenance personnel expenses.
g.With RS485 communication interface function, it can realize the network operation and monitoring functions of the energy-saving system.