Your body is part of the environment you perceive and act upon. Your hands are in the visual field, you have constant haptic and proprioceptive information about your own surfaces, edges and apertures. So the child's body is itself a permanently available field of affordances.
A fingernail presents a graspable edge, which affords biting and pulling. A nostril is perfect for fitting a child's finger, and again, affords insertion. Dried mucus affords removal.

An important part of this is the active exploration phase of perception. The organism moves, touches, mouths and manipulates to pick up information, and children are in an intense phase of exploratory learning. The mouth is one of the earliest perceptual organs. Infants quite literally explore objects by mouthing them before they explore them manually.
Nose picking and nail biting are exploratory behaviours turned on the self. The child is picking up information about the textures, boundaries and sensations of their own body.

As for why these habits can carry into later phases of life is quite simple --- it brings them satisfaction.