A basic induction variable of a loop is a variable b defined in a statement of the form b := b + n or b := b - n where

n is a constant, and

b has no other definitions in the loop.

Knowing the induction variables is very useful. For instance, they may allow us to replace multiplication by addition (often by a constant) [0]

[0] http://www.csd.uwo.ca/~moreno/CS447/Lectures/CodeOptimization.html/node14.html