Scattering parameters describes the input-output relationships between ports in an electrical system. Specifically at high frequency it becomes essential to describe a given network in terms of waves rather than voltage or current. Thus in S-parameters we use power waves.

In RF design, we cant use other parameters for analysis such as Z,Y,H parameters as we can't do short circuit and open circuit analysis as it is not feasible.

For a two port network, s-parameters can be defined as

S11 is the input port voltage reflection coefficient

S12 is the reverse voltage gain

S21 is the forward voltage gain

S22 is the output port voltage reflection coefficient

The S-parameter matrix can be used to determine reflection coefficients and transmission gains from both sides of a two port network. This concept can further be used to determine s-parameters of a multi port network. 

These concepts can further be used in determining Gain, Return loss, VSWR and Insertion Loss.

Return Loss can be thought of as a measure of how close the actual input/output impedance of the network is to the nominal system impedance value.

VSWR is defined as,                                 VSWR