There are a number of changes that were made in Wind Waker HD. For the casual player, playing as intended, the two main differences to consider are the removal of the Tingle Tuner, and the addition of the Swift Sail.
The Swift Sail is an upgrade to the sail that automatically sets the wind direction, and also allows the King of Red Lions to go significantly faster than with the normal sail. The Swift Sail can be found in the Auction House on Windfall Island after beating Dragon Roost Cavern. It's not required, but it makes sailing so much faster and easier.
A change that affects fewer players, the removal of the Tingle Tuner, means just that: you cannot use the Game Boy Advance to assist your gameplay whatsoever (most walkthrough will probably assume that you do not have the equipment to use the Tingle Tuner anyway). The Tingle Statues, however, are still in the game, but Link can now use his own bombs to reveal the chests they are in, instead of needing to use a Tingle Bomb.