The F value is a value on the F distribution. Various statistical tests generate an F value. The value can be used to determine whether the test is statistically significant.
The F value is used in analysis of variance (ANOVA). It is calculated by dividing two mean squares. This calculation determines the ratio of explained variance to unexplained variance.
The F distribution is a theoretical distribution. There are many of these distributions, and each of them differs based on the degrees of freedom.
The F value and the degrees of freedom of the sources of variance are used to determine the probability of the F value. The probability is the significance value for the test.