A time series x_t is called to be nonstationary if its statistical properties depend on time. The opposite concept is stationary time series. Most real world time series are nonstationary.
An example of a nonstationary time series is a record of readings of the atmosphere temperature measured each 10 seconds with some random errors that have a constant distribution with zero mean. At any given time point the mean of the readings is equal to the true temperature. On the other hand, the mean value itself changes with time – as far as the true temperature varies with time.