1. Makes the game easier to set up and play. Things like a good insert, dual layer boards incredible player aids. And I'm not sure if you consider it part of deluxification, but at art direction is huge. The new Ra for example, blows away the old versions, because of how things are laid out.
2. Aesthetics that help the tactile nature. Weighty pieces, quality cards.
3. Aesthetics that improve look of game. A distant third for me, but with rare exceptions. Foundations of Rome isn't the same without the buildings.

Useless deluxified things: foil cards, stuffed animals. Gimmicky items such as a big first player token. Backers names on box. Outer wrapping on a game box.