The rate of natural increase, most simply, is the difference
between the birth rate
and the death rate
in a given population
One calculates the crude birth rate (the number of births per 1000 population in a given year), and the crude death rate (the number of deaths per 1000 population in the same year), and subtracts the latter from the former. The result is the rate of natural increase. If the result should be negative, one can say that it is the rate of natural decrease or, more simply, a negative increase.
The purpose in expressing the rate of natural increase, and not just the net number of people added to, or subtracted from, the population, is to show be able to compare large and small populations.
Such things matter particularly to biologists and geographers.