There are two cases in which a normal tuning will not suffice to make the piano sound like it has been tuned normally. In these cases, extra tuning is required.
1) The piano has not been tuned in a very long time and is severely out of tune, and/or
2) You require a pitch correction, which usually entails a procedure normally known as a pitch raise.
In both cases a first tuning pass is necessary to set the tension of the piano into the right neighborhood before the piano can be properly tuned with a normal tuning. Note that in most cases this situation only occurs after the piano has been neglected for a long time and is not part of normal maintenance.