Change of transconductance for MOSFET
The transconductance is the ratio of the relative change of current to the relative change of gate-source voltage.

Looking at the black line of your graph, the current at VGS=4.25 is 0.6A and at VGS=4.5V it is about 1.1A. 

The transconductance is given by gm=(1.1A-0.6A)/(4.5V-4.25V)=2A/V.

So, it can be used to have a linear expression to calculate the change of current for a change of voltage around the point where the transconductance was calculated.