A square is a polygon that looks like this.


It has FOUR equal sides and a right angle at each corner.
To find the area of a square, we raise the length of a 
side , to the 2nd power, i.e., 

The practice of finding the area of a square became
known as "squaring".  Thus the practice of raising a number 
to the second power became to be known as "squaring".

A quadratic equation has as its largest power of a variable
the 2nd power.

There is a similar story about cubes and cubic equations.

A cube is a solid figure that looks like this:

 

To find the volume of a cube, we raise the length of a 
side , (actually it's called an "edge") to the 
3rd power, i.e., 

The practice of finding the volume of a cube became
known as "cubing".  Thus the practice of raising a number 
to the third power became to be known as "cubing".

A cubic equation has as its largest power of a variable
the 3rd power.

Edwin