This article is from the RSC/UKSC Cricket FAQ, by Ganesh with numerous contributions by others.
Someone [promoted up the order] to increase the
rate of scoring. Often these players aren't expected
to be there for too long, [just there to score some
quick runs and relieve the pressure.] The term comes
The batting side [...] can afford to lose a pinchhitter
without putting them in too much trouble.
As Micheal Holdings was probably the first to point
out, a pinch-hitter he has a role to play in test matches
too. The 30-60 rapid runs that one expects from him, can
turn the course of a low-scoring, tension-ridden test match.