Density-independent deaths are those deaths caused by an event that is not related to the population density in which the deaths occurred. For instance, death by lightning strike would be density-independent because the chance of a lightning strike does not increase when there are more people in that area.
An example of density-dependent deaths would be an epidemic of influenza. The influenza virus travels from person to person, so if there are more people in an area there are more that can become infected and therefore more that can die from influenza. In rural areas, where population density is low, influenza tends to be stopped because there aren't enough people to keep the infection going.