These two details perform the function of contributing to the mystical, other-worldly nature of the "belle dame sans merci" by presenting her as a "faery's child," as the speaker suggests. Note how these two details are attached to her. Firstly, the knight tells us how this strange, mystical lady found "roots of relish sweet, / And honey wild and manna-dew" with which to feed him. Manna is an allusion to the heavenly food that God provided to sustain the Israelites during their wandering in the desert, and thus we associate it with supernatural food, which greatly augments the supernatural status of the lady.
Secondly, the knight tells us that this lady took him to her "elfin grot," which makes it sound as if it were an abode for elves or other magical creatures of fantasy. Both details therefore serve to highlight the way that this lady is not of this world, and belongs to another supernatural and mystical world of magic and enchantment. This is of course something that the knight quickly learns himself as he falls victim to the lady's spell.