If you are into fine dining, I am sure you have seen black truffle being grated by the waiter on top of your food in a Micheline star restaurant. It's one of the most expensive edible mushrooms in the world.
As for what it's doing in a cosmetic product, it's a great question and we cannot say that there are tons of great research papers out there giving a reliable answer. What we could find is a patent application claiming that a cosmetic product with black truffle extract can fight reactive oxygen species (aka antioxidant), it can improve blood flow by expanding the capillary blood vessels and it can inhibit skin irritation.
Other tiny bits of infos we could piece togeather say that Tuber Melanosporum Extract works as a humectant (water-binding) moisturizer or that it's good (but not very good) as an antioxidant, anti-aging and anti-inflammatory agent.