1. It is forbidden to derive any benefit from the Chanukkah lights, even if it is for a holy purpose, such as to learn by its light. The custom is to place an additional light – called a “shamosh” (attendant) – nearby, so that if someone uses the illumination of that area, they will be using the light of the shamosh rather than the sanctified Chanukkah lights. The shamosh should be placed separate from the other lights to make it obvious that it is not one of Chanukkah lights. The shamos his lit in case one inadvertently comes to benefit from the illumination of that area, but ideally one should not rely on the light of the shamosh and even its light should not be used (Shulchan and Mishnah Berurah673).
2. The reason it is forbidden to use the illumination of mitzvah lights is to make it clear that they were kindled specifically for a mitzvah. Others say that since the miracle of Chanukkah occurred with the Menorah, the Sages ordained that the Chanukkah lights we kindle should be treated akin to the Menorah whose illumination was not to be used (ibid.).
