Functional test is to power on the assembled PCB board with firmware programmed in.
This is to dig out some hidden problem which escaped from the inspection in AOI and X-ray. This is best safe option to make sure customer to receive the ordered PCB assemblies at correct quality.
In WELLER, commonly we suggest customer to accept our request to firmware and power on their boards to implement a electrical function test, and do repair once some defects found at our house accordingly. So as that all the problem can be killed at our own house and not let them go to customer. Rather than other supplier who do not do any recommendation of functional test and the projects sometimes catch file when customer power on their boards after receipt.