Stationary data are data for which the probability distribution of points remain invariant with a slide across the time axis. That means that moments are invariant across the time axis.

Non-stationary time series have changing distributions and therefore moments across the time axis.

Autoregressive modelling is based on the use of stationary models without which no reliable forecasting may be done.

Simply, being stationary reduces the number of parameters and the complexity of the model. In addition, the estimation is much easier in the stationary time series.

You should read through econometric textbooks.