Linked from
The 15 pages that link to Cross-validation, each with the reason it gives.
OverfittingRelated: Repeated held-out estimates help detect overfitting and select model settings.
ResidualRelated: Out-of-sample residuals measure prediction errors beyond the fitted observations.
Ridge regressionRelated: It is commonly used to choose ridge regression's penalty strength.
Data scienceRelated: It tests whether a fitted model generalizes beyond its training data.