In Shampoodle's in "Animal Crossing: New Leaf," Shampoodle's has an extra seat next to the one you sit in. What is it for?
A lot of the shops in New Leaf have a whole lot of decoration, and this is no exception. The parlor would look quite empty with only one chair. The chair does in fact not do anything in the game mechanically.
It doesn't do anything. The Shampoodle shop wouldn't look good with one chair. Your character can sit on it but Harriette will not style your character's hair when sitting on that chair.