Signal processing refers to the broad study of how we can transform, manipulate, and gain important information about signals, both analogue and digital.
Nowadays analogue circuits are used when interacting with the environment, and digital circuits are used for internal computations and signal processing.1 As digital circuits exclusively deal with binary signals, they tend to be much simpler than analogue signal processing circuits, and are thus more reliable and economic than analogue circuits.
Pretty damn near close to magic.