According to Hamilton (1994), page 1-5:
suppose a process where: y(t) = b x 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.
However, as far as I know the term is far more common for VEC models. Hope this helps a bit.