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.
These details serve to emphasize the supernatural elements of the poem. More than that, they are details that put the knight in a particular relationship with the fairy. There is a tradition that casts the fairy as a temptress that bewitches the knight -- in short, that her love for the knight is a trick of some sort. One way to understand the manna and "elfin grot" are as domestic details -- the fairy is caring for the knight in a particular way. Most readers see the knight as an adult and the fairy as a child, but these details suggest the opposite, or at least that there is a mutual dependency of the two. It's not clear whether we can understand the fairy's love for the knight -- if indeed she does love him -- as genuine, or part of a trick. The dream, in which he is warned of being "in thrall" to the fairy, is a sort of dream-within-a-dream, and its relationship to the truth is as problematic (or more so) as the rest of the poem. What is clear is that, at the end, when the knight wakes on the "cold hill's side," there is sadness and a palpable sense of loss.