"To explain the variations" means to provide an explanation or description for the differences or changes that exist between different things or situations. Full definition
The research considered whether other measures of socioeconomic status did a better job of explaining variation in pupil achievement at primary and secondary school. (schoolsweek.co.uk)
A common critique of climate models is that they can not explain these variations in the data. (niskanencenter.org)
First, what explains variations in paleo climate does not have to be the same thing that explains current climate change. (skepticalscience.com)