Rainbow technology allows for massive amounts of digital data to be stored using colors and geometric shapes printed on paper. It works by encoding files like text, images, videos into colored circles, triangles, and squares with high density storage of up to 2.7GB per square inch. The data is encoded through a process that converts bits into unique values linked to specific color combinations, adds error correction bits, and prints the encoded data for storage and later decoding back into the original files. This provides extremely high capacity and low-cost data storage on a simple paper medium.