If we are talking about the world as a whole (as opposed to any particular country) there are three main variables that can be used to predict population growth. However, we must realize that there are other variables that would come into play if we were trying to predict population growth as accurately as possible.
The three main variables are birth rate, death rate, and the composition of the population in terms of age. Birth rate, of course, is the rate at which children are being born. This must be known so that we can know how many children are likely to be born to replenish the population. Death rates are the rates at which people die each year. This affects the population because each death reduces the population.
It is also important to know the age structure of the population. A population that has many people who are over the age of thirty is likely to have less population growth than one that has many people who are in their early teens or younger. This is because the thirty year-olds are getting to the end of their most likely reproductive years while the younger people are just reaching theirs.
There are other variables that matter, such as the income trends in the various countries of the world. However, these three are the basic variables that matter the most.