First, even though you shut down your pc, the power supply is still plugged into the wall outlet (mains) and the psu is still turned on. Try turning off the psu and see what happens. The on/off switch is located on the back of the power supply.
Some power supplies have a built in thermostat that keeps the psu fan spinning until the psu cools down. Eventually the psu fan will stop. Does your psu fan eventually stop? Does the fan stop when you turn off the power supply?
Some motherboards have onboard led's that remain on even when the pc is turned off. My motherboard has its own power switch and reset switch. Both switches on the motherboard are illuminated. Even though I turn off the pc those switches remain lit. The lights turn off if I turn off the power supply.
These situations are normal and there is no harm. The psu fan and led's on the motherboard use very very little power. It is insignificant. However, if you turn off the power supply and the psu fan keeps spinning, then you have a problem.