What specifically does an ANOVA of a linear model tell you?

[magicnumbers]

I got this explanation from the SAS support website:
Performing an analysis of variance (ANOVA) on a linear model enables you to assess the model effects on the variation in the response. The overall ANOVA analyzes the significance of the entire model.

I am hoping someone can supplement this with further details, because I am still confused.

FYI, I am running an anova on a linear model in R, but I just want to understand what the results actually mean.

[victorxstc]

If the ANOVA P value becomes significant, it is indicative of the presence of at least one independent variable in the model which is significantly correlated to the dependent variable. So the model is useful. Otherwise, if the ANOVA P > 0.05, the model should be excluded.

[noetsi]

A signficant ANOVA for OLS means that the model adds signficant predictability to your model. That is you can predict Y correctly more often compared to a model with no predictors in the model.