Wikipedia says:

Aleatoric uncertainty, aka statistical uncertainty, which is unknowns that differ each time we run the same experiment. For an example of simulating the take-off of an airplane, even if we could exactly control the wind speeds along the run way, if we let 10 planes of the same make start their trajectories would still differ due to fabrication differences. Similarly, if all we knew is that the average wind speed is the same, letting the same plane start 10 times would still yield different trajectories because we do not know the exact wind speed at every point of the runway, only its average. Aleatoric uncertainties are therefore something an experimenter cannot do anything about: they exist, and they cannot be suppressed by more accurate measurements.
Epistemic uncertainty, aka systematic uncertainty, which is due to things we could in principle know but don't in practice. This may be because we have not measured a quantity sufficiently accurately, or because our model neglects certain effects, or because particular data are deliberately hidden.

http://en.wikipedia.org/wiki/Uncertainty_quantification