The transformer is probably 9V, it's just slightly higher when no load is connected.
The LED is just there to show it's charging.
When no battery is connected the voltage across the 5R resistor is zero so the LED is off.
When a battery is connected some current flows through the 5R resistor so a voltage appears across it so the LED turns on.
The 100R resistor limits the current through the LED to a safe level.
I suggest you measure the resistor again, it's probably higher than 5R, with 215mA flowing the voltage will only be 1.075V which isn't enough to turn on an LED.