A broad concept concerning lack of knowledge, especially the absence or imprecision of quantitative information about a process or population of interest.
Uncertainty is a broad concept referring to lack of knowledge and ways to model that lack (such as with probability distributions of model parameters), as well as quantitative evidence thereof, such as measures of variation or dispersion in data.
In one specialized field, uncertainty is defined by the BIPM Guide to the Expression of Uncertainties in Measurement as:
parameter, associated with the result of a measurement, that characterizes the dispersion of the values that could reasonably be attributed to the measurand
Uncertainty should not be confused with error. The error is the actual difference between the measured value and the true value. The error is usually not known; if it were known, it could be corrected. The uncertainty is rather an estimate of the statistical distribution of errors around the true value. For example, one might repeat a measurement 100 times and the 100 measurements will have mean a certain mean and standard deviation. The mean could be the reported measurement, and the standard deviation the reported measurement uncertainty.