In Romans' time, a cohort of legionnaires consisted of a group of soldiers sharing the same military events for a certain period of time. In epidemiology we consider that a cohort consists of people belonging to the same population and sharing similar experience for a defined period of time.
Cohort studies involve the comparison of disease incidence over time (risk or rate) between two subsets of a population (two cohorts). One of the 2 cohorts is exposed to a certain characteristic (exposure). The other is not. All other things being equal between the two cohorts but for their exposure. In both cohorts we measure occurrence of disease over the specific study period. However whenever the condition of "all other things being equal" is not met, the comparison might be wrong.
The following graph adapted from Rodrigues  illustrates occurrence of cases over time in the two cohorts. Initially Ne persons are exposed and Nu persons are unexposed. The number of persons who are disease free decreases over time (shaded area). The number of cases (non shaded area) increases over time but more in the exposed cohort. At the end of the study, respectively Ce and Cu cases have occurred in the exposed and unexposed cohorts. The shaded area represents the cumulative time during which persons were at risk of developing disease in each of the cohorts during the entire follow up period.
In this example, the Risk of disease in the exposed cohort (Re) = Ce / Ne and the Risk of disease in the unexposed cohort (Ru) = Cu / Nu.
In a cohort study, we can compare those 2 risks, in order to see if exposure has an effect on the risk. One comparison is to look at the difference: Re-Ru is also called the risk difference. The risk difference shows us what the absolute increase (or decrease) of the risk is when exposure occurs.
Another comparison is to see how the relative increase (or decrease) occurs after exposure: this is the Risk Ratio: Re/ Ru. This is also called 'Relative Risk'.
In addition to risks, we can also measure rates in cohort studies: in such a situation, the observation time in the cohort is taken into account in the denominator (for example: 51 cases per 1200 person-years). When we compare the rate of cases in the exposed cohort with the rate of cases in the unexposed cohort, then we consider that a Rate Ratio.
1. Rodrigues L. Kirkwood BR. Case-control designs in the study of common diseases: updates on the demise of the rare disease assumption and the choice of sampling scheme for controls. Int J Epidemiol 1990 Mar:19(1):205-13