Many statistical procedures have some sort of underlying model for which you fit parameters based on your data. If there were no noise this might fit your data precisely, but in practice there is a difference between the value predicted by the model and the actual data points; this difference is called the residual.
For example, suppose you are performing a user study and have pre-tested the skill level of users with a value between 0 and 10. You measure their task completion time for a particular task and then calculate a linear regression to obtain a best fit line: time = 50 – 2*skill_level. Although this is a best fit line, it does not fit every user perfectly. Perhaps Aled has a task completion time of 43 seconds and a skill level of 8. The model would predict a time of 50 – 2*8 = 34 seconds; the difference of 9 (43–34) is the residual.
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