A single train/test split gives you one estimate of performance, which might be lucky or unlucky. K-fold CV partitions the data into k folds and rotates the validation role across them, giving k estimates (one per fold) instead of one, plus a sense of their spread.
Every point gets to be in the validation set exactly once. The mean across folds is a much more reliable estimate than any single split, and the std shows the spread of fold scores. Because folds share training data, that spread is only a rough stability indicator, not a formal confidence interval.
Caveat: if you use these CV scores to pick the polynomial degree, the winning score is optimistically biased. For an honest estimate of the chosen model, use nested CV or a separate held-out test set, and fit any preprocessing inside each training fold to avoid leakage.