Melamine is a nitrogen-based plastic that is used to create a variety of products from utensils, plates and cups to dry-erase boards, and, most importantly for furniture, countertops and as a finish on MDF, particle- and chipboards. (MFC, in particular, stands for melamine-faced chipboard.)
It is scratch- and moisture-resistant and hard enough to withstand everyday use, so boards with a melamine veneer are used to construct shelves, cabinets, desks and more. It protects the board, especially MDF, from spillages, that would otherwise damage it. Melamine can also be coloured, giving it great versatility, or patterned to imitate solid wood.
Health concerns were raised regarding melamine when it was illegally added to milk formula in 2008. It is known to be a health hazard when ingested, and studies have shown that it can leak into hot or acidic foods (e.g. orange or tomato juice) when used as a container. However, this leakage was well below any levels of concern, and used as part of furniture, even in the kitchen, melamine should be perfectly safe. (Source)
Image by Laidler139 on Wikimedia Commons