Biotin has been seen as the go-to vitamin for beauty ever since one pilot study in women with brittle nails showed supplementation to be beneficial. It is currently being marketed for improving nail, skin, and hair aesthetics. These claims, however, were not followed up scientifically so there is not much evidence to support biotin's role here. It can plausibly have these actions mechanistically, but there is simply not much evidence that can be used as support.
Overall, aside from instances where biotin may be deficient (alcoholism, some epileptic drug therapies, and overconsumption of raw egg whites) the supplement does not have any solid evidence for benefits and may have a role as a beauty supplement pending better evidence.