Explanation rimes with interpretation, not with statistics or analyses. Statistical analyses do not explain anything - only give us probabilities that may or may not strengthen our beliefs. To get away from the confusion other terms have been suggested, such as "extracted variance". This is not a semantical matter - words do matter, like the poet said: Words are just the shapes that let the feeling through (John Gorka). 

So R-square is not explained variance, moreover it is not the effect size but an estimate of the effect size. When you ar not working with population data, then you have a sample and you are estimating the population value. So get a confidence interval for your effect size. How? You don't get it in SPSS automatically. Ever wondered why the "Bootstrap" button in the SPSS menu-dialogs is for? Here is a Bootstrap CI for R-squared (R script) that does the job.