Susceptibles have been exposed to neither the wild strain of the disease nor a vaccination against it, and thus have not developed immunity.
However, except in some special cases such as malaria, these individuals make up such a small proportion of the total population that they can be ignored for the purposes of modelling an epidemic.
To understand the rationale behind this relation, think of A as the length/amount of time spent in the susceptible group (assuming an individual is susceptible before contracting the disease and immune afterwards) and L as the total length of time spent in the population.
The advantage of estimating S in this way is that both the average age of infection and life expectancy will be well documented, and thus the other parameters needed to calculate S will be easily at hand.
Reasons for this are varied and may include suppression by the host immune system, or abortive measures taken by intrinsic cell defenses.