The health of individuals is highly heterogeneous, as is the rate at which they age. To account for such heterogeneity, we have suggested that an individual's health status can be represented by the number of health deficits (broadly defined by biological and clinical characteristics) that they accumulate. This allows health to be expressed in a single number: the frailty index (FI) is the ratio of the deficits present in a person to the total number of deficits considered (e.g. in a given database or experimental procedure). Changes in the FI characterize the rate of individual aging. The behavior of the FI is highly characteristic: it shows an age specific, nonlinear increase, (similar to Gompertz law), higher values in females, strong associations with adverse outcomes (e.g., mortality), and a universal limit to its increase (at FI ~0.7). These features have been demonstrated in dozens of studies. Even so, little is known about the origin of deficit accumulation. Here, we apply a stochastic dynamics framework to illustrate that the average number of deficits present in an individual is the product of the average intensity of the environmental stresses and the average recovery time. The age-associated increase in recovery time results in the accumulation of deficits. This not only explains why the number of deficits can be used to estimate individual differences in aging rates, but also suggests that targeting the recovery rate (e.g. by preventive or therapeutic interventions) will decrease the number of deficits that individuals accumulate and thereby benefit life expectancy.