What is the difference between a transitory and a permanent shock?
"Permanent shock" is a shock whose effects on current values of a variable never die out in absolute terms. "Transitory shock" is a shock whose effects gradually die out. Consider the simplest one-lag model

$$y_t = \beta y_{t-1} + u_t, \;\;\; y_0 = 0$$

By direct substitution one gets that 

$$y_T = \sum_{t=0}^{T-1}\beta^t u_{T-t} = u_T + \beta u_{T-1} + \beta^2u_{T-2} +...+\beta^{T-1}u_1$$

If $|\beta| &lt;1$ the absolute effect of say shock $u_1$ on $y_T$ diminishes as time passes, $T \uparrow$. While mathematically it doesn't die off completely except at infinity, its absolute contribution decays exponentially.  

On the other hand, if $\beta =1$ (a "unit root" model) then

$$y_T = \sum_{t=0}^{T-1}u_{T-t}=u_T + u_{T-1} + u_{T-2} +...+u_1$$

and no matter how far we move into the future the shock at period $1$ will fully contribute to the value of $y_T$.

Of course, if autocorrelation is strong (high $\beta$) then a "transitory" shock will influence visibly many periods in the future, so it may be "ignored" when examining "long-term" outcomes, but not when one deals with mid-term effects and policy.