Nose-picking is the act of extracting mucus or foreign bodies from the nose with a finger. Compulsive nose-picking is known as rhinotillexomania (etymology: Greek, rhino "nose" + tillexis "habit of picking" + mania).
Although a very common habit, it is a mildly taboo subject in most East Asian and Western cultures. Children's literature often makes reference to it, to amuse readers (for example Jacques Charpentreau's poem "De l'Education!" and Gordon Korman's Nose Pickers series). John Allen Paulos's imaginary novel, Rucker: a life fractal has a section where "proboscis probing is discussed at length." 
Mucophagy is the consumption of the mucus thus extracted, and is commonly referred to as "picking your nose and eating it" (where 'it' refers to the mucus rather than the nose). While common in some cultures, it is also generally viewed as a cultural taboo, to the extent that many of those who engage in the practice generally find it disgusting when done by someone else in their presence, much like flatulence.
However, at least one well-known doctor sees nose-picking and mucophagy as beneficial . He states that not only is the finger capable of reaching parts of the nose that a handkerchief or tissue is unable to, thus keeping the nose cleaner, but that eating the bacteria-rich dried mucus offers a boost to the immune system, and is analogous to immunization.
Due to the special nature of the blood supply to the nose and surrounding area, it is possible for retrograde infections from the nasal area to spread to the brain, although this scenario is unlikely to arise from nose-picking. For this reason, the area from the corners of the mouth to the bridge of the nose, including the nose and maxilla, is known to doctors as the "danger triangle of the face".
Rhinoliths forms when the mucus traps dust and other particles in the air. Mucus dries around the particle and hardens, somewhat like a pearl forming in an oyster. Since catching foreign particles is one of the main functions of nasal mucus, the presence of rhinoliths is a good indicator of a properly functioning nose (as opposed to a "runny nose", which can indicate illness).