Second moment of inertia is a property of a surface measuring its area distribution from its neutral axis.
In engineering it is closely related to bending moment resistant.
Let's see why:
In materials with linear stress/strain ratio, with a constant modules of elasticity like steel, wood, plastic, metals, the deformation of section along depth of the beam is linear and plain surfaces remain plain with a small angle of rotation theta.
Therefore the strain along the depth for a small differential surface is linearly increasing e= y tan(theta) hence it's proportional to y and the stress is proportional to y da.
But this differential element stress must be multiplied by its distance from the fulchrum, neutral axis, to find the contributory moment.
y.y da = y^2 da.
Sorry, but my phone doesn't have fancy fonts to display math.