Zach Gemignani discusses the challenges of big data communication, emphasizing the importance of design principles for effective data visualization and communication. He outlines seven key principles: gradual reveal, compactness and modularity, guiding attention, supporting casual use, leading to action, relevance, and providing explanations before presenting information. The overarching goal is to simplify the data communication process, making it as intuitive as sharing a photo on social media through their technology platform, Fruition.