Descendants are the children of supernatural creatures. They are typically a second-generation supernatural and are only allowed at the school because they have inherited the gene from their ancestor. Some fall under more than 1 category depending on how much of their ancestors power/traits they have received.
For a child to be classed as a descendant they must be half-human, half-supernatural and have inherited enough of their supernatural ancestor powers in order for them to be a danger in human society. However Descendants are never as strong as their ancestor as they only inherit half of their power.
The exception to this rule are creatures who's powers are passed down through generations, for example werewolves, witches and banshees.