Residual
Residual turns up in 2 fields: tides, statistics. Here is what it means to the people in each one.
Residual in tides
The observed water level minus the predicted tide, showing the effect of weather, rivers and other non-tidal causes.
What is left after the astronomical prediction is subtracted from the observed record. Residuals carry storm surge and set-down, pressure effects, river floods, seasonal changes and any sensor or datum problems. Forecasters track the residual to warn of flooding, and analysts check it after harmonic work: a residual that still shows a tidal rhythm means the analysis missed something.
"Residual's been plus 0.4 all day with the onshore wind, so tonight's high will top the prediction by about that."
Residual in statistics
Difference between an observed value and the value a fitted model predicts for it.
A residual is what the model failed to explain for one data point: observed minus fitted. Plotting residuals is the main check on any regression or ANOVA. Against fitted values they should form a shapeless band; a funnel means variance grows with the mean, and a curve means a missing term. Against run order they should show no trend, and on a normal probability plot they should fall near a straight line.
"Residuals fan out above 300 nm, so the error isn't constant. Try a log transform before you trust those p-values."