What does this equation mean?

The UN Population Division builds its projections using the cohort-component method : rather than extrapolating total population, it starts from the population by single year of age and sex in a base year, and ages every cohort forward one year at a time by applying age-specific and sex-specific survival probabilities (mortality), age-specific fertility rates applied to women of reproductive age (which generates the next year’s births), and net international migration assumptions applied by age [ 1 ] . Formally, for an age group a in year t : $P_{a+1,t+1} = P_{a,t}\, S_{a,t} + M_{a,t}$. where $P_{a,t}$ is the population in age group a at time t , $S_{a,t}$ is the survival rate applied to that cohort, and $M_{a,t}$ is net migration entering or leaving that age group during the interval. Births are generated separately by summing age-specific fertility rates across women of childbearing age, then applying infant survival to place the new cohort at age zero the following year. Iterating this recursion one year and one cohort at a time, across every age group and both sexes, is what actually produces the projected pyramid for a future year — not a single equation fit to a historical growth curve [ 1 ] .