What is Normalized DC Current Gain (as oppossed to DC Current gain)?
"Normalised" means  "relative to some specified reference value".

In this case the Y axis = 1 when Ic = ~~ 7 mA. This means that somewhere else they will have specified the gain AT 7 mA. This graph allows you see see how the gain varies realative to the gain at 7 mA as Ic is varied.

At 0.1 mA and at 100 mA the Y axis value is 0.5 so we know that the gain is 0.5 x the value at 7 mA.

Why they chose 7 mA as their reference point I know not.

They could have just used actual gain BUT normalized \$h_{FE}\$  shows you better how a typical device behaves, regardless of the actual gains, which can vary widely between different devices of the same given transistor type.