If the moment of inertia is known for an object about a given axis through the center of mass, the parallel axis theorem tells you how to find the moment of inertia for that object for any axis parallel to the given one.
The PAT tells you how the MI of an object changes when you use an axis that's not through the cm. Obviously, the mi will be higher (imagine trying to turn a disc around a point on its circumference - or even on the end of a long massless pole)
There is an analogous situation with standard deviation of a probability distribution. It is a 'second moment', in the same way. The standard deviation from the mean is less than the rms deviation from some other value. Also, the power of an AC waveform is greater when it has a DC offset component. Same sums for all three, basically.