Before revision: The bilinear transform is a special case of a conformal mapping (namely, a Möbius transformation), often used to convert a transfer function of a linear, time-invariant (LTI) filter in the continuous-time domain (often called an analog filter) to a transfer function of a linear, shift-invariant filter in the discrete-time domain (often called a digital filter although there are analog filters constructed with switched capacitors that are discrete-time filters).
After revision: The bilinear transform is a special case of a conformal mapping (namely, a Möbius transformation), often used for converting a transfer function of a linear, time-invariant (LTI) filter in the continuous-time domain (often named an analog filter) to a transfer function of a linear, shift-invariant filter in the discrete-time domain (often named a digital filter although there are analog filters constructed with switched capacitors that are discrete-time filters).