Hector's Mode is an odd mode, acting as a sort of "Director's Cut" to Eliwood's Mode. HM follows the same events, but fromm the perspective of Eliwood's more uncouth friend, Hector. This mode shows different sides and depths of the story, including the final fate of the Lycian Aliiances leader, his older brother Lord Uther, and the origin of the mysterious Magic Seal Kishuna.
While similar in story, Hector's Mode ramps up the difficulty quite a bit, changing enemy composition from the get-go, and introduces several chapters unique to it, allowing for three charatcers who were not recruitable in Eliwood's Mode. It's hard mode is the hardest setting in the game, and in considered by fans to be one of the franchises biggest challenges.
