According to *Hamilton (1994)*, page 1-5:

suppose a process where:
$y_{t} = b \times y_{t-1} + w_{t}$

Where $y_{t-1}$ is the realisation in the previous period and $w_{t}$ is some random innovation.

The long run effect therefore is the effect on $y_{t+1}$ from a permanent increase in $w$. Hence the long-run effect is ${1}/{(1-b)}$ for this special case (or the expected value of the function).

However, as far as I know the term is far more common for Vector Error Correction models. Hope this helps a bit.