Uncertainty expresses the extents of the range within which a value can exist, quoted as a distribution about some nominal value. The magnitude(s) of the uncertainty in any given situation can be influenced by (for example) the calibration accuracy of an instrument, or the numerical precision of a calculation.
Unlike tolerance, the concept of uncertainty carries no connotation of acceptability: it simply expresses the way things are, not the way they’re supposed to be. It must be accounted for in verification activities, such that the limits of (aggregated) uncertainty lie within the tolerance limits of a requirement.
See also Experimental Uncertainty.