Finding the root of a function y(x) refers to finding values of x for
which y(x)=0.

This is often used as a method of solving equations. For example, consider the
equation

x - 4 = 2.

One method of approaching this might be to reformat the equation so that one
side of the equation is equal to zero. Subtracting the 2 from both side in the above
example would give us

x - 6 = 0.

This particular example is fairly trivial, but suppose you have the equation

x^{2} + x = 6.

This could be reformatted as

x^{2} + x - 6 = 0

or

(x + 3) (x - 2) = 0

and the equation can be easily soved by inspection.