Easy mode is unlocked after completing the main game in Golden Sun: The Lost Age (it isn't available in the original Golden Sun). When starting a new file you will be asked to choose a game mode. With easy mode you start at the level your Adepts were at the end of the main game. All enemies will retain their original stats as well. It also transfers all your money, EXP and any permanent stat increases (such as those gained by consuming Apples), from the completed file to the new game. This makes it possible, although very tedious, to maximise all stats on all characters. It does not transfer items or Djinn however. Therefore, in order to obtain all Djinn (and hence gain access to Anemos Inner Sanctum), a transfer is required, which, if not done before agreeing to play on Easy Mode, will override the original Golden Sun's character's stats. If, however, the transfer is completed before choosing a Lost Age Clear Data file for Easy Mode, then Isaac's party will join Felix's with the stats from the Lost Age Clear Data.
It should be noted that your characters will not have the same Psynergy when you start a game in Easy Mode. For example, Jenna starts off with only her Flare and Fume Psynergies. This is only temporary, however, and once you obtain Echo, or change your equipment, all your Psynergies will be returned.