A modular form is a highly symmetric function that appears in an ostensibly separate area of mathematical study called analysis. Because they exhibit so many nice symmetries, modular forms can be easier to work with. And all of these objects should also have a partner in the broader world of symmetric functions like modular forms. So they focused on a particular type of abelian surface, called an ordinary abelian surface, that was easier to work with. If they could show that the same set of numbers could also be derived from a modular form, they’d be done.