This article is from the Piano Purchase and Maintenance FAQ, by Isako Hoshino email@example.com with numerous contributions by others.
"Aural" tuning is how piano tuners have traditionally tuned
instruments -- tuning strictly "by ear." Usually after a
reference note is established, tuners adjust the pitches of
all the other notes based on the reference note without
relying on anything else other than their ears.
Sometimes, instead of setting pitch "A" to a reference,
tuners will simply set that "A" to whatever pitch it's at
(which may be too high or too low because of seasonal or
other factors) and then tune the rest of the piano relative
to that pitch. This avoids having to drag all the notes very
far up or down in pitch with each change of season, with
consequent tuning instability or, in the extreme (where the
pitch is very low), possible string breakage.