Degrees of freedom represent the difference between: (a) the number of data points, N; and (b) the number of parameters being estimated.
The "overall" or "Total" df for an ordinary ANOVA is N - 1, because, at that level, you are estimating one parameter, the grand mean (mu). So, with N observations, only N - 1 of them are "free to vary" if you impose the constraint that all N must either sum or average to a specific value.
In statistics, the number of degrees of freedom is the number of values in the final calculation of a statistic that are free to vary. The number of independent ways by which a dynamic system can move, without violating any constraint imposed on it, is called number of degrees of freedom.