Derived demand is the demand for a factor of production that comes about because of demand for the thing that is made from that factor of production. The factor of production is not demanded for its own sake, but because it is necessary for the production or distribution of the product that is demanded. Let us look at a couple of examples.
First, we can look at the demand for transportation. (This can be seen as a factor of production as it relates to a finished good because transportation is needed to get a good from the place where it is made to the place where it is purchased.) We do not really demand truck and train transportation per se. Instead, what we demand is the goods they carry. Because we demand consumer goods, there is also derived demand for the transportation systems that bring them to us.
Second, we can look at the demand for teachers. In general, people do not really want teachers. What they want is education. However, at this point, teachers are needed to provide education. Therefore, the demand for teachers is derived from the demand for education, which is the service that teachers provide.