It's ably explained in Roberts' opinion. In short, Congress often left the fine details to the agencies, not least because the laws were often drafted within those same agencies. Chevron was based on the idea that if statutory text is ambiguous the people in charge of implementing said statute were best positioned to figure out what it meant, in accordance with the Administrative Procedures Act (which sets out rules for for how agencies make rules, eg requiring consultations, publications of proposed rules, public comment periods thereon etc.).