To use when our aim is to solve an ODE (of any order) only with reduction of order method. If you just want to solve an ODE use the tag differential-equations.
If the ODE is second order we have the general form $y''+p(x)y'+q(x)y = 0$ and we use reduction of order when we are given (or we can guess) a solution $y_1$. Then we suppose $y_2$ depends on $y_1$ by the following : $y_2 = v(x)y_1$. Then we differentiate this expression and substitute in. We will use $z'=v$ to reduce the order afterwards.
