Inverse density dependence is a positive-feedback situation in which an environmental factor which affects population density inversely changes when the population density changes, such that an increase in population density will cause the population's growth to improve, while a decrease in population density will cause the population to not grow as well.
Generally, the environmental factor affects birth and death rates to cause this to occur.
For example, for some species (such as humans), the more individuals there are, the better they are able to defend themselves as a group from predators (the environmental factor).
Another example would be pack animals (such as hyenas) which have better foraging/hunting success (and therefore better pup survival rates) as the pack grows larger.
Still another example would be a species that is better able to find mates and produce young as the population gets larger, but which is less able to find mates as the population decreases (thus exacerbating the species' population decline).