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Partial eta-squared is a measure of variance, like r-squared. It tells us what proportion of the variance in the dependent variable is attributable to the factor in question. You can get these measures by choosing the 'Estimates of effect size' option when setting up an ANOVA.
1 Despite what I say about rules of thumb for eta squared and partial eta squared, I reiterate that I'm not a fan of variance explained measures of effect size within the context of interpreting the size and meaning of experimental effects. If you only have one predictor then, eta squared and partial eta squared are the same and thus the same rules of thumb would apply. 2  If you have more than one predictor, then I think that the general rules of thumb for eta squared would apply more to partial eta squared than to eta squared.