this is about Linear System Theory (what they now call Signals and Systems). in either continuous-time (often called "analog") or discrete-time (often called "digital") systems, you have three fundamental blocks:
1. adder (or subtracter), sometimes called a "summer". it adds two or more signals together.
2. scaler (sometimes called "gain"). it multiplies a signal by a constant or coefficient.
3. some form that can discriminate between signals with respect to frequency.
3a) in analog systems, usually that device is represented as an integrator and has Laplace transform of 1/s
3b) in digital (DSP) systems, that device is represented as a unit delay and has Z transform of 1/z
you assemble these adders, scaler, and integrators or delays using one of several forms. the most common forms are the Direct Form I (DF1) or Direct Form II (DF2), but you'll see other forms. from those forms and from knowledge of the coefficients, you get a transfer function that fully describes the input/output relationship in a linear, time-invariant system.