Depends on the technology. Most all of the modern ones use light based technology either Fiber Optic Gyros or Ring Laser Gyros. Basically you literally measure the transit time of light thru a know path length. The variance from the nominal time to transit the path length is proportional to the rotational rate of the gyro spool.
The older electro mechanical gyros use the exact same principal as a toy gyroscope. You take a proof Mass momentum wheel and spin it at a known angular speed to set up a specific angular momentum. If you rotate the gyro momentum wheel about its input axis it generates a “precession torque” about its output axis which again is proportional to the input rate.
There are all kinds of other types like semiconductor MEMS (micro electronics mechanical system ) which use semiconductor proof masses on a monolithic silicon substrate, quartz rate sensors which generate a signal voltage proportional to the strain energy in a proof crystal which is again proportional to input rate, and there is a really cool emerging technology called hemispherical resonant gyro or HRG which is very similar to a wine glass resonance excitation.
So basically the device measurement package generally provides some kind of output generally proportional to the rotational rate of the device about its input axis. And then we get to how they all work in what is called the “inertial frame”. But generally they all have some sensing mechanism which applies specific physical properties, such conservation of momentum to the speed of light, which provides as output measurement proportional to the rotational input rate.
Sorry you asked yet or you want me to go on?