ANOVA tests to see if the means you are comparing are different from one another. It does not indicate how different means are from one another. The difference may be very large, or it may be very small.
Effect Size helps us estimate how large any difference we find may be.
Here's a sample ANOVA question and its source table:
Researchers want to test a new anti-anxiety medication. They split participants into three conditions (0mg, 50mg, and 100mg), then ask them to rate their anxiety level on a scale of 1-10. Are there any differences between the three conditions using alpha = 0.05?
The most common measure of effect size for a One-Way ANOVA is Eta-squared.
Using Eta-squared, 91% of the total variance is accounted for by the treatment effect.