What does "inertial" refer to in "inertial reference"?
It is called inertial, because it works by measuring—and integrating—inertial forces¹, that is forces due to acceleration of the reference frame (i.e. the aircraft). Gyroscopic effect used to measure rotation is also due to inertial forces.
The measured forces include gravity², which can't be easily separated, but this is done by observing that the speed is limited, so the average acceleration must be zero and therefore the long term average equals gravity.

¹ In general relativity the inertial forces are usually considered as real as any other, so the term “fictitious” is not really appropriate.
² In general relativity gravitational force is considered an inertial force. In standard English terminology, gravity also includes centrifugal force due to rotation of Earth.