It is very similar to other port parameters like ABCD, Z, Y, etc. S-parameter deals with incidence and reflected power waves and the 2 port parameters are ##S_{11},\; S_{21},\;S_{12},\;S_{22}## and with certain condition like either the reflected or incident wave is zero etc. Keep that in mind, it's just another parameters.
Most RF device are spec with S-parameters. They are presented either as polar coordinates form where they give you the amplitude and the phase angle, or presented as complex numbers. You plot the parameters on Smith Chart and you can read out Z and Y parameters also. That will make it very easy to design circuits and matching networks.