Normality is the assumption that the underlying residuals are normally distributed, or approximately so.
While a residual plot, or normal plot of the residuals can identify non-normality, you can formally test the hypothesis using the Shapiro-Wilk or similar test.
The null hypothesis states that the residuals are normally distributed, against the alternative hypothesis that they are not normally-distributed. If the test p-value is less than the predefined significance level, you can reject the null hypothesis and conclude the residuals are not from a normal distribution. If the p-value is greater than the predefined significance level, you cannot reject the null hypothesis.
Violation of the normality assumption only becomes an issue with small sample sizes. For large sample sizes, the assumption is less important due to the central limit theorem, and the fact that the F- and t-tests used for hypothesis tests and forming confidence intervals are quite robust to modest departures from normality.
