Ans: Engineers are interested in pressure drop and heat transfer. Pressure drop is an important quantity to know because we pay for it. More the pressure drop more pumping power must be provided hence more energy is required. The additional energy comes from burning fuels most of the time which is not cheap.
It becomes easier to calculate pressure drop when we know the friction factor (internal flow) or skin friction coefficient (external flow).
In a similar way, once engineers know the Nusselt number (Nu), it becomes easier to calculate heat transfer.
The Reynolds/Chilton-Colburn analogy connects pressure drop with the Nusselt number. That is analogies connect fluid mechanics with heat transfer
If you know pressure drop you can calculate heat transfer or if you know heat transfer you can calculate pressure drop.