It is now more than 40 years since the BIPM outlined the current harmonised approach to the expression of uncertainty in measurement, and 30 years since the publication of the Guide to the Expression of Uncertainty in Measurement. Despite several decades of use and application to a wide variety of measurements, there remains a lack of clarity about the purpose of measurement uncertainty. The lack of clarity is most clearly reflected in the inconsistency in the way uncertainty is used and reported. The lack of a clear statement of purpose is also an impediment to the teaching of good measurement practice. This paper investigates a range of applications of measurement uncertainty to identify and illustrate the purposes of measurement uncertainty, and to understand its proper usage and reporting. Two broad purposes for uncertainty are identified: one relating to decision making and utilising expanded uncertainties to characterise the range of values attributable to a measurand, and one relating to the modelling of dispersive effects in measurements and utilising standard uncertainties as the measure of dispersion. Expanded uncertainties are used at the ends of traceability chains to make inferences about the measurand and ensure decisions can be made with appropriate confidence. Standard uncertainties are parameters in measurement models characterising the unpredictable aspects of measurement processes and are propagated along traceability chains to ensure meaningful inferences and decision making. Suggestions for improvements to uncertainty guides and for the usage and reporting of uncertainty are provided.